Preheat the oven to 400 degrees.
Heat a small cast iron skillet over medium heat then add the butter. Remove from the heat as soon as the butter is melted.
Crack the eggs into the skillet then drizzle the top of them with the heavy cream.
Next, sprinkle the minced parmesan, shallot, and thyme leaves on top of the eggs. Season with sea salt and freshly cracked pepper, to taste.
Place into the oven and bake for 4-6 minutes, or until the whites are just set but the yolks are still soft.
Remove from the oven and sprinkle with fresh parsley. Serve immediately with buttered toast, if desired. Enjoy.