Pat watermelon cubes completely dry with paper towels and set aside on a clean kitchen towel to air-dry further while you prepare the dough, about 15 minutes.
In a medium saucepan, combine water, butter, 2 tablespoons sugar, and salt. Bring to a rolling boil over medium-high heat, stirring occasionally until butter melts completely.
Remove from heat and add the sifted flour all at once. Stir vigorously with a wooden spoon until the mixture forms a smooth ball and pulls away from the sides of the pan, about 1 minute.
Let the dough cool for 5 minutes, then beat in eggs one at a time, mixing until fully incorporated and glossy before adding the next. Stir in vanilla extract until the dough is smooth and pipeable.
Transfer dough to a piping bag or large zip-top bag with a corner snipped off to create a 1/2-inch opening. Heat oil in a large, deep pot to 350°F on a candy thermometer.
Take one watermelon cube and pipe dough around it in a spiral motion, completely encasing the fruit with a thin, even layer about 1/4-inch thick. Repeat with remaining watermelon.
Working in batches of 3-4, carefully lower churros into hot oil using a slotted spoon. Fry for 3-4 minutes, turning once, until deep golden brown on all sides. The dough should be crispy and puffed.
Remove churros with a slotted spoon and drain on paper towels for 30 seconds. Immediately roll in the cinnamon-sugar mixture while still hot.
Let cool for 2-3 minutes before serving so the watermelon center cools slightly and won't burn mouths. Serve warm for the best contrast between crispy shell and juicy fruit.
