Preheat your oven to 450 degrees F. Coat a cast iron skillet or springform pan with butter. If using a springform pan, cover the bottom with a piece of parchment paper.
Grate the sweet potatoes with a box grater or the grater attachment of your food processor. Transfer the grated potato into a large mixing bowl.
Use paper towels to squeeze the excess liquid from the potatoes.
Add the egg, salt, and pepper to the potatoes. Stir until well combined.
Pour the potatoes into your prepared pan. use your hands to press the potatoes up the sides of the pan and along the bottom to create a crust. Be sure to close any holes that may appear while moving around the potatoes.
Bake for 30 minutes. The top edges of the crust will brown and the rest of the crust will crisp up.
Carefully remove the pan from the oven and allow to stir for 5-10 minutes.
Reduce the oven to 350 degrees F.
While the crust sets, heat a skillet over medium-high heat. Cook the bacon until crispy. Remove to a paper towel-lined plate.
Place the spinach in the hot bacon fat for 1 minute, just enough to wilt it a bit. Remove the spinach from the fat.
In a large mixing bowl, whisk together the eggs and milk. Add the spinach, bacon, and goat cheese to the egg mixture. Stir to combine.
Pour the filling into your crust.
Bake the quiche for 30 minutes. Carefully remove from the oven, and let the quiche set for 10 to 20 minutes.