Combine the lemon slices, sugar and vanilla in a resealable container; cover and shake vigorously until the lemon slices are coated. Set aside, shaking occasionally, until the sugar dissolves, about 30 minutes. Smash the lemon slices with a fork to release the juices. Let sit 30 minutes, then refrigerate until ready to use.
Fill 2 martini glasses with ice and set aside. Shake the lemons again, then strain the juice into a liquid measuring cup. Combine the vodka, vermouth, pear nectar and 1 1/2 ounces of the lemon syrup in a cocktail shaker. Fill with ice and stir until cold. Discard the ice in the martini glasses and strain the drink into the chilled glasses. Garnish with pear slices and lemon twists.
Photograph by Levi Brown