Preheat the oven to 425 degrees F. Set flatbreads on a large rimmed baking sheet.
Melt butter in a small skillet over medium heat. Add the mushrooms, garlic powder, and sea salt. Cook for 4-5 minutes, stirring occasionally, until the mushrooms are dark brown. They should release their moisture and that should simmer off.
While the mushrooms cook, brush olive oil lightly along the outer rim of the flatbreads. Sprinkle the mozzarella evenly on top.
When the mushrooms are ready, scatter them on top of the mozzarella. (They will be hot and start to melt the mozzarella right away, so try to arrange them more or less as you want them, so you don’t have to move them a lot and pull off the cheese.) Sprinkle Parmesan and basil lightly on top.
Transfer flatbreads to the oven and bake for 9-12 minutes, until the cheese is melted and bubbling in spots, and the exposed edges are brown and crisp.
Remove from the oven. Sprinkle with more basil and red pepper flakes, as desired. Slice and enjoy!