Adjust oven rack to middle setting. Preheat oven to 400ºF and place a baking sheet in the oven while it heats.
Heat oil in a large skillet over medium heat. When oil is hot, add sliced mushrooms. Cook, stirring occasionally, until tender and the liquid they've released has evaporated.
Add garlic and cook for an additional minute. Then add the spinach and cook until wilted and the pan no longer looks wet. Remove from heat.
Press thawed pie crust into a deep, 9-inch pie pan with a removable bottom (or a deep-dish pie pan). Transfer spinach and mushroom mixture into crust and top with half of the cheddar cheese.
In a large bowl, whisk eggs, half-and-half, salt, and pepper. Pour egg mixture into the crust and top with the remaining cheese.
Place the filled quiche on the preheated baking sheet. Loosely cover the pan with aluminum foil and bake for 40 minutes. Remove the foil and continue baking until the quiche is set and the crust is golden brown, another 10 minutes.
Let the quiche rest for 10 minutes before serving.