Seckel pears, discovered in the nineteenth century near Philadelphia, may be the only pears native to the United States.
Put enough pears into a 48-ounce glass jar to fill. Add vodka. Seal jar, and let stand at room temperature 2 weeks (up to 2 months).
Heat sugar and 1 cup water in a medium saucepan over medium-high heat, stirring until sugar has dissolved. Add rosemary; remove from heat. Let stand 30 minutes. Discard rosemary. Let cool completely.
Fill 12-ounce glasses halfway with ice. Add 4 tablespoons vodka, 2 tablespoons syrup, and 3 tablespoons pear nectar to each. Top with 1/2 cup sparkling water. Serve garnished with rosemary sprigs.
Syrup can be refrigerated in an airtight container up to 1 month.