In a small saucepan, bring sugar and water to a boil, stirring until sugar has dissolved. Turn off heat and add mint; steep for 15 minutes. Strain syrup through a fine-mesh sieve into a small bowl; discard mint solids. Refrigerate mint syrup until cold, 15-20 minutes.

Purée melon, lime zest, lime juice, salt, and mint syrup until smooth, in a blender. Transfer to a large bowl and stir in cream and tequila; cover and refrigerate for 2 hours.

Churn melon mixture in an ice cream maker according to manufacturer’s instructions.

Meanwhile, chill a loaf pan in the freezer until ice cream is done churning. Transfer ice cream to chilled loaf pan, wrap in plastic wrap and foil; freeze for at least 2 hours.