For the ganache, chop the chocolate into small pieces and place them in a medium sized bowl. Then, heat the milk and golden syrup until they just begin to simmer (around 180°F or 82°C). Pour the heated liquid over the chocolate and let it sit for 30-60 seconds. Then, whisk until all of the chocolate has melted. Add in the espresso powder and the softened butter and blend with an immersion blender or whisk until the ganache becomes glossy and creamy. Set aside to come back to room temperature while you make the ice cream.
For the ice cream base, use a hand or stand mixer to whip the heavy cream into soft peaks. While it's whipping, measure out the irish cream, coffee liqueur, and vanilla into one bowl and the espresso powder and kosher salt into another. Then, slowly add the sweetened and condensed milk 1/3rd of a can at a time. Continue whipping in-between additions to bring the mixture back to soft peaks.
In the same slow, incremental manner pour in the remaining ingredients; espresso and salt first then the liquids. This will give the solid ingredients time to dissolve into the ice cream.
Once you have added in all of the ingredients and brought the ice cream base back up to soft peaks, you are ready to combine the ice cream and the ganache into a final container to freeze.
This step is also done in thirds. Pour 1/3 of your base into the container and spread it around. Then spoon 1/3 of your ganache in a thin layer and use a long utensil like a chopstick or offset spatula to gently swirl the ganache and base together. The point is to spread it around not mix it in. Less is more. Repeat these steps with the base and ganache twice more, until you have used everything.
Once layered, place the Dublin mudslide no-churn ice cream into your freezer for at least 6 hours. Because of the booze, it takes a little longer to harden.
Scoop when frozen and enjoy.