Place rack in the center of your oven and preheat oven to 350 degrees F. Lightly coat a 9-inch pie dish with cooking spray.
If your chicken is not yet cooked: Cook and shred chicken, following these easy steps.
Heat the olive oil in a large skillet over medium heat. Add the broccoli and peppers and sauté until they are beginning to soften, about 5 minutes. Add the green onions, garlic, salt, and pepper and cook 1 additional minute. Remove from heat and set aside.
In a large bowl, whisk together the eggs, then add cheese, chicken, and the vegetables from the skillet. Stir to combine, then pour into the prepared pie dish. Bake 40 minutes, until the center is nearly set and a toothpick inserted comes out clean. The frittata will puff while baking, then settle a bit as it cools. Let sit 5 minutes then serve warm or at room temperature.