Preheat oven to 350°F. Generously coat a 12-cup muffin tray with cooking spray; set aside.
Heat oil in a large nonstick skillet over medium-high. Add ham; cook, stirring often, until starting to brown, 3 to 4 minutes.
Add mushrooms and bell pepper; cook, stirring occasionally, until softened, about 4 minutes.
Add scallions; cook, stirring constantly, until softened, about 30 seconds. Remove from heat, and let cool for 5 minutes.
Meanwhile, whisk together eggs, ricotta, Parmesan, salt, pepper, and ¼ cup Fontina in a large bowl until thoroughly combined.
Stir in cooled ham mixture. Divide mixture evenly among prepared muffin wells (about ¼ cup each). Top evenly with remaining ¼ cup Fontina.
Bake until egg bites are puffed and set, 14 to 16 minutes, rotating muffin tray halfway through baking time.
Let egg bites stand for 5 minutes before removing from muffin tray. Sprinkle with Parmesan, and serve hot.
