While the oven is preheating, add olive oil to a medium sized skillet over low to medium heat. Allow the olive oil to heat for a minute, then add minced garlic. Cook the garlic for about a minute until browned and aromatic.
Next, add chopped broccoli and mushrooms to the skillet. Cook for about 5-8 minutes, until the broccoli and mushrooms become tender. Drain any water that may have developed. Set the garlic broccoli mushroom aside for now.
Place a pie crust into a 9 inch pie dish. Spoon the garlic broccoli mushroom mixture into the pie dish.
In a medium sized bowl, whisk together a large egg and a tablespoon of milk. Brush this egg wash mixture over the edges of the crust to help it brown.
Add three more eggs into the same bowl, and whisk until beaten. Generally, you’ll need four eggs to make quiche. I didn’t want to waste the egg wash so I added it into the quiche. Now, pour milk and shredded cheddar into the bowl then whisk until combined. Pour this mixture over the broccoli and mushrooms.
Sprinkle parmesan cheese on top.
Bake the broccoli mushroom cheddar quiche for about 45 minutes until the crust has browned and the filling looks solid.
Allow the quiche to cool down before slicing into it.