1. Preheat oven to 425 degrees. In a medium bowl, whisk together eggs, cream, milk, cayenne, herbs, and half the cheese. Season with salt and pepper.

2. In a small ovenproof nonstick or cast-iron skillet, cook bacon over medium, stirring occasionally, until crisp, 7 minutes. Transfer bacon to egg mixture and pour all but 1 teaspoon fat into a small bowl. Add 1 pita round to skillet and cook until toasted and golden, 3 minutes, flipping halfway through; transfer to a plate. Repeat with more reserved fat and remaining pita half; leave pita in skillet, cut side up.

3. Add egg mixture and cook over medium, gently stirring, 30 seconds. Top egg mixture with other pita half, cut side down; transfer to the oven and bake 8 minutes. Sprinkle evenly with remaining cheese, then bake until frittata is puffed and golden, about 8 minutes. Let sit 3 minutes, then cut into wedges and serve warm.