In a large skillet or sauté pan with sides, heat 2 tablespoons of olive oil on medium-high heat. Add the broccoli, onions and garlic. Sauté until crisp-tender, about 4 to 5 minutes. Remove from heat.
In a large mixing bowl, add the eggs, ¼ cup olive oil and Greek yogurt. Whisk to blend.
Add the flour, baking powder, salt, Parmesan and cheddar. Add black pepper, to taste, if desired. Mix well to combine.
Add the broccoli mixture. Stir to combine.
Evenly spread the batter into an 8x4-inch loaf pan that's been lined with parchment paper.
Bake at 350 degrees F for about 50 to 60 minutes, or until bread passes the toothpick test. (If the loaf is getting too brown on top, you can cover it loosely with aluminum foil.)
Allow loaf to cool to room temperature before slicing and serving.