Preheat oven to 350 degrees F. Coat a 9-inch pie pan or cast iron skillet with oil spray.
Squeeze excess moisture from spinach and place in prepared pie pan.
In a bowl, whisk eggs and milk together. Add mustard, thyme, salt, pepper, and nutmeg and whisk well. Pour the egg mixture over the spinach. Top with cheddar.
Carefully transfer to the oven and bake until the mixture is set in the center, approximately 30 minutes. Remove from the oven and let cool 5 to 10 minutes. Cut into 6 wedges and serve.