Measure out and cut the butter and shortening for the dough into 1/2in (1.25cm) cubes. Then, put them in the freezer while you prep everything else.
For the filling, simmer the maple syrup in a small saucepan over medium low heat for about 5 minutes. Then, increase the temperature to medium-high or high. Use a thermometer to bring the maple syrup to between 220-240°F (104-115.5°C) for 2-3 minutes. The lower end of the temperature range will make a mostly set, slightly oozy filling while the higher range will help produce a set filling once fully baked and cooled. The maple syrup will bubble and foam quite a bit, just let it.
By now, the syrup should have reduced down to roughly 1 cup (320ml). If you have a bit more, just pour to the measurement needed. If you have slightly less, don't worry. It won't affect the filling. Turn off the heat and set the syrup aside.
Next, add the butter for the filling to a small saucepan on medium heat. Make sure to continuously stir or swirl the pan as the butter melts and then froths. When you see the milk solids turn a light brown color, turn off the stove and move the pan from the heat. The butter will continue to cook and should end up a nice warm brown. When the brown butter cools a bit, add it into the maple syrup and whisk them together until incorporated. Set aside and move onto pastry prep.
For the pastry crust, add the flour, sugar, and salt to a food processor and pulse 3-4 times until fully mixed. Fill a small bowl roughly 1/3rd of the way with ice; then add water until the ice floats off the bottom of the bowl. Give the ice and water a good mix to make sure it's very cold and set aside.
Now, take the butter and shortening out of the fridge and add to the food processor. Pulse into the flour mix (3-4 times) until small pea-sized pieces form. At this point, you can slowly add the ice water a tablespoon (15ml) at a time.
As you add water, you will see the dough lose its sandy texture and turn yellow as the flour hydrates. You should need between 5-6 tablespoons (75-90ml) of ice water to bring the dough together. To test if it's ready, take off the top of the processor and pinch some of the dough between your fingers. If it sticks together, you can stop there. If it's still a little sandy and falls apart, add some more water.
Once you have your dough ready, you want to keep it as cold and unworked as possible. Dump the dough out onto a lightly floured surface or onto wax paper. Lightly press the dough into a ball and then cut it in half (≈285g per half). Quickly and gently make each piece into a log that can easily be cut into 6 equal pieces. Do not overwork the dough; try to work quickly, as the heat from your hands will melt the butter and the dough will not turn out as flakey.
Wrap the pieces in plastic wrap and let rest in the fridge for a minimum of 90 minutes and up to 24 hours. Resting the dough allows the gluten to relax and hydrate, which makes rolling it out much easier.
When ready, return to the filling. With a spatula, not a whisk (it adds too much air), mix in the brown sugar, salt, vanilla extract, lemon zest, and eggs until completely incorporated. If you are using lemon juice, add that now as well. Place the filling in the fridge until it's time to pour it into the tarts.
When your filling is made and your dough is rested, preheat your oven to 425°F (240°C).
Then, take a dough log out of the fridge and cut out 6 equal pieces. They should be roughly 44g per piece. Cover the pieces you aren't working with, so they don't dry out. One at a time roll out a disk to a little more than 5in (12cm) in diameter and cut out a circle of pastry dough between 4.5-5 in (11-12cm). Fit the pastry circles into muffin cups making sure that the dough goes all the way to the bottom of the cups and is flush to the walls, where the dough doesn’t overlap or ribbon near the top. Repeat with the other pieces and then with the second log of dough.
When your tart cups are ready, take the filling out of the refrigerator and mix it again to re-distribute the brown sugar which will have settled to the bottom. Then fill each dough cup ⅔ to ¾ full with syrup mixture. Bake on bottom rack of the oven for 20 to 25 minutes. Keep an eye on the surface layer of the filling. It will puff up into a dome and turn a medium-dark brown. When the top breaks and bubbles the tarts are ready.
Take the maple butter tarts out of the oven and cool them for 10 minutes. Then, try spinning each tart (still in the tin) 360° by gently pushing in a circular motion with your fingers positioned at their top and bottom. If you can gently spin the tarts as they cool, they will be easier to remove later. If you have a few tarts that won't spin after cooling for 10 minutes, give the crust another 30 minutes more to set and use a sharp paring knife to slide between the tart and the tin. Then try spinning again.
Make sure the tarts are completely cool before removing them from the pans. You can do this by either popping the tarts out with an offset spatula or paring knife OR you can gently flip the muffin tin over and let the tarts fall out, turning them over as you go.