Preheat oven to 350 degrees F (175 degrees C). Place squash on a baking sheet, cut-side down.

Bake in the preheated oven until the outer shell of squash is tender, about 45 minutes. Scoop fibers and seeds out of squash and discard. Shred the tender squash meat with a fork; measure 3 cups and place in a bowl.

Heat olive oil in a saucepan over medium heat; saute onion and garlic until onion is transparent, 5 to 10 minutes. Add spinach, black pepper, and oregano; cook and stir until heated through, about 3 minutes. Add spinach mixture to squash.

Whisk eggs together in a bowl; add milk and whisk until frothy. Pour egg mixture over squash mixture; mix well.

Spray a 9-inch pie pan with cooking spray.

Sprinkle bread crumbs into prepared pie pan. Pour squash-egg mixture over bread crumbs.

Bake in the preheated oven until a knife inserted into the center of the quiche comes out clean, about 45 minutes.