Combine 2 teaspoons sugar and warm water in a cocktail shaker; stir to dissolve sugar. Pour Meyer lemon juice, lemon peels, vodka, and orange liqueur into the shaker; add ice. Cover and shake vigorously.
Remove a lemon peel from the shaker and wipe the rim of a martini glass with the peel. Dip the rim of the glass in 1 teaspoon sugar, or as needed. Strain martini into prepared glass.
Two teaspoons of simple syrup can be used to sweeten the martini instead of the sugar and water. To make 1 and 1/2 cups simple syrup, bring 1 cup white sugar and 1 cup water to a boil until sugar is melted. After cooling the syrup, store it in the fridge. It will keep several weeks.
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