Preheat oven to 450°F. Prepare four parchment hearts.
Arrange mango slices over half of parchment paper. Divide shallots, chile rounds, and ginger over mango; divide scallops over top. Season generously with salt and pepper. Drizzle 1/2 tsp. vanilla over each batch of scallops; dot with butter. Top with a slice of lime, then seal.
Arrange the packets on two large baking sheets. Bake 10 minutes, switching pan position halfway through. Transfer packets to plates with a wide spatula. Slit tops; gently open. Serve with the black beans and tortilla chips.