In a medium mixing bowl, whisk the eggs, heavy cream, salt, and pepper until the mixture is homogenous and slightly aerated.
Heat olive oil in a 10-inch non-stick skillet over medium heat until shimmering.
Add the sliced mushrooms to the skillet and sauté for 5 minutes until browned and moisture has evaporated.
Incorporate the baby spinach into the skillet and toss until the leaves are just wilted, approximately 1 minute.
Reduce heat to medium-low and pour the egg mixture over the vegetables.
Using a silicone spatula, gently move the eggs from the outer edges toward the center to form soft, large curds.
Once the eggs are 80 percent set, sprinkle the shredded cheddar cheese over the surface.
Remove the skillet from heat and allow the residual temperature to finish cooking the eggs while the cheese melts.
Serve immediately for optimal texture.