While mushrooms are cooking, mix eggs with heavy cream and salt and pepper.
Preheat oven to 350F
Add spinach to pan and stir until all spinach has wilted. While stirring, mix in a pinch of salt and pepper with the thyme to the mushrooms and spinach.
After spinach has wilted, turn off the heat and pour in egg mixture.
Gently stir eggs with spinach and mushrooms.
Top with shredded cheddar cheese and bake for 20 minutes.
The frittata will be very puffy when removed from the oven and will slowly deflate.
Optionally, top with more thyme and allow to rest 10 minutes before serving.