Cut watermelon into cubes and make sure to cut the rind off. (Weight out slightly over a pound of watermelon chunks.)
Place watermelon chunks into the blender and puree until completely smooth, when no little chunks remain.
Strain the watermelon puree through a fine mesh strainer. (Swirl the puree in the strainer with a spoon if it needs more help straining.)
At this point, you can make the cocktails right away or store the watermelon juice in the refrigerator for later. **
Watermelon Mojito method 1:
Take mint leaves off the stem and add them into the cocktail shaker. Squeeze lime juice into the shaker as well and add simple syrup.
Use a muddler to gently press on mint leaves just a few times. (The point to to bruise and muddle the mint, not mash it into a pulp!)
Pour in rum, watermelon juice, add a little ice, and shake it all together for a few seconds.
Add crushed ice into four highball glasses, about half way full, and divide the mixture evenly among the glasses. (Remember to leave room for club soda.
Add 2-3 oz of seltzer water to each glass, gently stir to combine and serve.
Divide mint leaves among the 4 highball glasses. Add 3/4 oz. lime juice and 3/4 oz. simple syrup to each glass.
Use a muddler to gently press on mint leaves just a few times. Repeat in each glass.
Add 2 oz. of rum and 4 oz watermelon juice into each glass and stir.
Add ice to each glass, top off with 2-3 oz of club soda and give each cocktail a gentle stir. Serve right away.
*This is the recipe to make 4 cocktails. To make one, combine 5-10 mint leaves, 3/4 oz. lime juice, 3/4 oz. simple syrup, 2 oz. silver rum, 4 oz. watermelon juice, and top it off with 2-3 oz. of club soda. **If you are not planning to make the cocktail right away, store fresh watermelon juice in a glass jar with an air-tight lid, in the refrigerator. Properly stored, it will last about 5 days. You can also freeze it in a freezer zip-top bag for up to 4 months. See the post above for more details.