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

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 plate. Repeat with more reserved fat and remaining pita half; leave pita in skillet, cut side up.

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