Preparation Bring sugar and 1 cup water to a boil in a small saucepan, stirring to dissolve sugar. Boil syrup for 2 minutes. Pour 1/2 cup syrup into a large pitcher. Add lime juice and 1/2 cup cold water. Set lime syrup aside. Transfer 1/2 cup remaining hot syrup to a small bowl. Add rosemary; let steep 15 minutes. Using a fine-mesh sieve, strain rosemary syrup into lime syrup; discard solids. DO AHEAD: Rosemary-lime syrup can be made 1 day ahead. Cover and chill. Scrape papaya flesh into a food processor; purée until smooth. Measure 3/4 cup purée (reserve remaining purée for another use, such as a smoothie); add to pitcher with rosemary-lime syrup. Add tequila; whisk to blend. Fill 4 large wineglasses with ice. Pour cocktail over. Garnish with zest and orchids (if using).
Preparation Bring sugar and 1 cup water to a boil in a small saucepan, stirring to dissolve sugar. Boil syrup for 2 minutes. Pour 1/2 cup syrup into a large pitcher. Add lime juice and 1/2 cup cold water. Set lime syrup aside. Transfer 1/2 cup remaining hot syrup to a small bowl. Add rosemary; let steep 15 minutes. Using a fine-mesh sieve, strain rosemary syrup into lime syrup; discard solids. DO AHEAD: Rosemary-lime syrup can be made 1 day ahead. Cover and chill. Scrape papaya flesh into a food processor; purée until smooth. Measure 3/4 cup purée (reserve remaining purée for another use, such as a smoothie); add to pitcher with rosemary-lime syrup. Add tequila; whisk to blend. Fill 4 large wineglasses with ice. Pour cocktail over. Garnish with zest and orchids (if using).