Preheat the oven to 375°F (190°C).
Lightly grease a jumbo muffin tin or individual ramekins.
In a large mixing bowl, toss the potato slices with olive oil or melted butter, garlic powder, dried thyme, salt, and black pepper.
Layer the potato slices into muffin cups, slightly overlapping them to create a stacked napoleon effect.
Sprinkle a small amount of Gruyere and Parmesan cheese between some of the potato layers.
Bake for 25–30 minutes until the potatoes are tender and beginning to turn golden.
Remove the pan from the oven and gently create a small well in the center of each potato stack.
Crack one egg into each well.
Add a small drizzle of heavy cream over each egg if desired.
Return to the oven and bake for 10–15 minutes, depending on how runny or firm you prefer the yolks.
Remove from the oven and let rest for 3–5 minutes.
Carefully lift each Baked Eggs Napoleon from the muffin tin using a spatula.
Garnish with fresh chives, parsley, and a light sprinkle of smoked paprika.
Serve immediately with Hollandaise sauce if desired.