Melt the butter in a nonstick skillet. Add the onions, garlic, and mushrooms to pan and cook 8 to 10 minutes or until soft. Add the flour, salt, basil and cayenne to the pan and cook for an additional 3 to 5 minutes. Remove from heat and set aside.
In a large bowl, whisk the eggs with the half and half, 1 cup of the cheese and the carrots. Add the mushroom/onion mixture to the egg/cheese/carrot mixture and stir to combine.
Slice 5 asparagus spears into 1-inch to 2-inch pieces. Lay the asparagus pieces on the bottom of the pie shell. Pour the filling over the asparagus in the pie shell.
Place the pie pan on the cookie sheet and bake for 20 minutes. Remove from the oven.
While the quiche is baking, slice the remaining asparagus spears into 1-inch to 2-inch slices or leave 5-inches long for a decorative design. Arrange tomato slices and asparagus pieces on top of the quiche in a wagon-wheel pattern or another attractive pattern.
Return the quiche to the oven and bake for an additional 20 to 30 minutes or until the quiche is firm to the touch and a knife inserted into the center comes out clean.
Sprinkle the quiche with the remaining 1/2 cup shredded cheese and parsley. Bake for an additional 10 minutes. Remove from the oven; let cool before slicing.