In a large bowl, whisk together the eggs, oats, cheese, parsley, dill, salt, and pepper. Add in the diced chicken, turkey, bell peppers, onions, and mushrooms. Mix until well combined.

Heat the olive oil in a non-stick skillet over medium heat. Add in the egg mixture and cook for 3-4 minutes, until the edges start to set.

Transfer the egg mixture to a baking tray lined with parchment paper. Use a spatula to shape the mixture into 12 muffin-sized portions.

Place the baking tray in the oven and bake for 15-20 minutes, until the eggs are set and the edges are golden brown.

Remove the egg muffins from the oven and let them cool on a wire cooling rack for 5 minutes. Serve warm.

To reheat, simply microwave the egg muffins for 30-60 seconds, until warmed through.