Make lemon oleo-saccharum (using the first 4 pieces of equipment) a day in advance of making the martini. While your finished oleo-saccharum is draining, collect your other ingredients and decide if you’d like to have a traditional sugared rim.
If that’s an emphatic “yes!", pour a small amount of agave onto a plate or into a shot glass. Hold your glass by the bowl and dip your paint brush into the syrup. Then paint the agave along the rim. When done, set the glass down and pour some sugar onto a small plate. Roll the adorned rim around in the sugar until coated. Set aside.
Next, measure and pour each of the martini ingredients into an empty shaker. Add whole ice cubes, close, and shake for 30-45 seconds.
Double strain into your prepared martini or coupe glass. Express a lemon peel over the glass and enjoy!
If you’d like to garnish further, consider a lemon slice or curled lemon peel.