Prepare Oven and Pan: Preheat your oven to 375°F (190°C). Lightly brush the 18 cups of a standard muffin pan with extra virgin olive oil.
Sauté Aromatics: Heat the remaining olive oil in a large skillet over medium heat. Add the diced shallots and bell pepper, sautéing for 4-5 minutes until softened and fragrant.
Wilt Spinach: Add the packed baby spinach to the skillet in batches. Stir continuously until all spinach has wilted completely, about 2-3 minutes. Remove the skillet from the heat and set aside to cool slightly.
Combine Fillings: In a medium bowl, combine the shredded chicken, rinsed Kalamata olives, chopped parsley, dill, lemon zest, and crumbled feta. Add the slightly cooled vegetable mixture from the skillet and stir until everything is evenly distributed.
Create Egg Emulsion: In a large mixing bowl, vigorously whisk together the whole eggs and egg whites until frothy and uniform in color. Sift the chickpea flour, Spanish paprika, turmeric, and black pepper over the eggs. Whisk again until no lumps remain, creating a smooth, cohesive egg mixture.
Assemble the Bites: Carefully spoon the vegetable and chicken filling evenly among the 18 prepared muffin cups. The cups should be about two-thirds full.
Fill and Bake: Gently pour the egg mixture over the filling in each cup, leaving a small amount of space at the top for expansion. Place the muffin pan on a baking sheet to catch any potential spills and bake for 18-22 minutes, or until the centers are set and the tops are lightly golden. A wooden skewer inserted into the center should come out clean.
Cool and Serve: Remove the pan from the oven and let the egg bites cool in the pan for 5-10 minutes. This allows them to firm up. To release, gently run a thin silicone spatula or butter knife around the edge of each bite, then lift it out. Serve warm or allow to cool completely for storage.