First step is to make a simple syrup. In a small saucepan, combine 1 cup of melon cubes, sugar and a few tablespoons of water. Heat to a simmer over medium heat. Simmer for 15 minutes, until the melon is completely softened and candied, and the juice is a syrupy texture. Filter through a strainer and set aside in a glass container.
For the cocktail: In a blender, combine the tequila, Cointreau, 2 cups melon cubes and lime juice. Add ice and blend to desired consistency. Pour into a chilled glass and garnish with mint and lime. Add some simple melon syrup to the top of the cocktail.