Set your oven to 375°F (190°C).
Lightly grease a 9-inch (apprx. 23cm) dish with cooking spray.
Warm oil in a large frying pan over medium heat.
Add the chopped onion and cook, stirring occasionally, until it begins to soften, approximately 3 minutes.
Stir in the garlic and cook for an additional minute.
Add the broccoli and cook, stirring, for about 2 minutes until it starts to soften. Remove the pan from the heat.
As a second step, in a large mixing bowl, whisk together the eggs, milk, sour cream, salt, and pepper.
Gently fold the broccoli mixture and shredded cheese into the egg mixture.
Pour the combined mixture into the prepared pie dish.
Bake in the preheated oven until the quiche is set and has a golden top, roughly 30 minutes.
Allow it to cool for at least 10 minutes before serving.