Preheat the broiler to 500°F and place a rack in the top third of the oven, about 8-10 inches away from the broiler.
Place watermelon wedges in a single row on a parchment-lined baking sheet.
Top each wedge with a square of cheese.
Place the baking sheet under the broiler just until the cheese melts and gets lightly tinged with golden brown, about 2-5 minutes. Watch carefully and rotate the pan if you notice a hot spot.
With a spatula, transfer the wedges to a serving platter and sprinkle with roasted almonds, place 2-3 mint leaves on each wedge, spoon a ⅛-1/4 teaspoon of olive oil over the top, and toss a pinch of flakey salt to finish.
Serve warm. This appetizer still tastes delicious when it cools off, so don't stress if it doesn't stay warm!