In a food processor, puree the watermelon until very smooth.

Strain the puree into a medium bowl using a fine-mesh strainer, pressing on the solids until you have 3 cups of juice.

In a medium saucepan, bring 1 cup of watermelon juice to a simmer over medium heat.

In a medium bowl, whisk 3 packets of gelatin and 1/3 cup sugar.

Whisk into the hot watermelon juice, stirring constantly until sugar and gelatin completely dissolve (2-3 minutes).

Gently stir in the lime juice and the remaining 2 cups watermelon juice.

Pour into a 9-inch square metal baking pan with 2-inch sides and refrigerate until set, about 2 hours.

In a small saucepan, bring 1/2 cup water just to a simmer over medium heat.

In a small bowl, whisk 1 packet of gelatin and 1/2 cup sugar.

Whisk into the hot water, stirring constantly until sugar and gelatin completely dissolve (2-3 minutes).

Transfer to a medium bowl.

Whisk in the yogurt and vanilla.

Let cool to lukewarm temperature.

Pour over the set watermelon gelatin and refrigerate until set, about 2 hours.

In a food processor, puree the chopped lime, cucumbers, and mint until very smooth, about 2 minutes.

Strain the puree into a medium bowl using a fine-mesh strainer, pressing on the solids until you have 2 cups of juice.

In a medium saucepan, bring 1 cup of cucumber-lime juice just to a simmer over medium heat.

In a small bowl, whisk the remaining 2 packets of gelatin and the remaining 1/3 cup sugar.

Whisk into the hot juice, stirring constantly until sugar and gelatin completely dissolve (2-3 minutes).

Add the remaining 1 cup of cucumber-lime juice.

Let cool to lukewarm temperature.

Pour over the yogurt gelatin and refrigerate until set, about 2 hours.

Fill a sink with about 1 inch of lukewarm water.

Place the pan in the sink and let stand just until the gelatin loosens from the pan, 10 to 30 seconds.

Gently loosen the gelatin from around the edges of the pan.

Invert onto a cutting board and remove the pan.

Using a knife, cut the gelatin into wedges.

Before serving, top with sesame seeds (if using).