First, prepare the gluten-free pie crust as directed.
Then chop the broccoli into bite-sized pieces. Chop the onion and dice the mushrooms and garlic, keeping the garlic separated. Set all ingredients aside.
Meanwhile, heat a pan on the stove on low heat. Once heated, pour in the tablespoon of olive oil. Then add in the broccoli, onion, and mushrooms. Cook until the veggies just start to soften, about 5-6 minutes, while making sure to stir them. Next, add in the diced garlic and cook just until fragrant. Turn off the stove and remove from heat.
Now, preheat the oven to 375°F. Place the pie crust pan on a cookie sheet lined with foil or parchment paper to catch any messes while baking.
Next, crack the eggs and place them in a mixing bowl. Use a whisk to beat them and pour in the milk, add in the salt, pepper, garlic powder, and cayenne. Continue whisking until all ingredients are combined.
Finally, pour the vegetables into the prepared pie crust and pour the egg mixture over the vegetables. Then bake in the oven on the middle rack for 45-50 minutes or until the quiche is set and the center does not jiggle. Allow the quiche to cool for roughly 10-15 minutes before serving.