6 cups diced honeydew, cantaloupe or watermelon
1/4 cup fresh lime juice, plus more to taste
1/2 cup sugar, plus more to taste
1 tsp fresh thyme leaves, plus sprigs for garnish
1/2 cup silver tequila or mezcal (optional)
Spread melon pieces on a rimmed baking sheet in a single layer. Freeze until just hard, about 1 hour.
Transfer melon pieces to a food processor and add lime juice, sugar, thyme, 1/2 cup water and tequila, if desired. Pulse until smooth and slushy, scraping the sides of the bowl occasionally. Add water if you prefer a thinner consistency. Add lime juice and sugar to taste.
Divide among serving glasses and garnish with thyme sprigs. Serve immediately with spoons, or let melt slightly to serve as a drink.