Step 1Using a paring knife, peel each apple in one long continuous peel. Set peels aside for garnish. Core the apples and cut into 1-inch dice.
Step 2Place the apple cubes in a blender with the lemon juice and simple syrup. Puree until smooth. Add additional lemon juice and simple syrup if needed for a puree that is slightly thicker than applesauce. Makes three-fourths cup. Use immediately; it will change color if left standing.
Step 3Combine 5 ounces vodka, 3 ounces apple liqueur, half the apple puree and 1 teaspoon lime juice in a cocktail shaker. Shake over ice until chilled. Strain into two chilled martini glasses through a fine mesh strainer to eliminate apple chunks, pressing with a wooden spoon to extract juices.
Step 4Hang half an apple peel spiraling over the rim of each glass for garnish. Repeat to make two more cocktails.