1. Preheat the broiler. Heat oil in a large skillet over medium-high heat. Add leeks and saute until just beginning to brown, about 2 minutes. Add garlic, mushrooms, prosciutto, red pepper flakes, salt and pepper and saute 30 seconds. Add broth and cook until almost all the liquid has evaporated, 2 to 3 minutes. Remove skillet from heat and stir in basil.
2. Place pitas on a baking sheet and top each with an equal amount of vegetable mixture and goat cheese. Broil 4 inches from heat for 1 minute, then rotate and broil 1 minute more.