Prepare the watermelon juice: Add the watermelon chunks to a blender and blend until completely smooth, about 30-45 seconds. Pour through a fine-mesh strainer into a large measuring cup or bowl, pressing gently with a spoon to extract all the juice while leaving solids behind.
Prepare the glasses: Run a lime wedge around the rim of each glass, then dip into the coarse salt to create a salted rim. Fill glasses with ice and set aside.
Mix the cocktail: In a cocktail shaker or large measuring cup, combine 2 cups of the strained watermelon juice, tequila, lime juice, and agave nectar. Stir well to ensure the sweetener dissolves completely.
Test and adjust: Taste your mixture and adjust sweetness or acidity as needed – add more agave if too tart or more lime if too sweet.
Add optional ingredients: If using jalapeño for a spicy version, muddle slices gently in the bottom of the cocktail shaker before adding other ingredients.
Pour and serve: Carefully pour the mixture into the prepared glasses, allowing the liquid to flow gently over the ice to maintain the salted rim.
Garnish beautifully: Add a small watermelon wedge and lime wheel to each glass. If using mint, add a sprig or two for aromatic garnish and visual appeal.