Melt butter in a medium saucepan over medium heat.

Add minced green onions and stir until wilted, about 1 minute.

Add water and salt; bring to a boil.

Gradually whisk in polenta.

Bring back to a boil.

Reduce heat to low and simmer until thick and creamy, stirring occasionally, about 13 minutes.

Stir in Parmesan cheese and thyme.

Season with salt and pepper to taste.

Cool the polenta until lukewarm.

Heat a large skillet over medium heat.

Add bacon slices and fry until beginning to brown but still pliable, about 4 minutes.

Transfer bacon to paper towels to drain excess grease.

Cool the bacon slightly.

Reserve 2 tablespoons of bacon drippings.

Line the sides of eight 1 1/4-cup custard cups with 2 slices of bacon each, forming a collar.

Place 1/2 slice of bacon on the bottom of each cup.

Divide the cooled polenta among the cups, about 1/3 cup each.

Press the polenta over the bottom and up the sides of the bacon.

Mix cheddar and Gruyere cheeses in a bowl.

Sprinkle 1/4 cup of the cheese mixture over the polenta in each cup.

Preheat oven to 400°F (200°C).

Crack 1 egg into the center of each cup.

Sprinkle the eggs with the remaining cheese, green onions, thyme, and black pepper.

Transfer the custard cups to a rimmed baking sheet.

Bake until the egg whites are almost set, about 20 minutes.

Let the eggs stand at room temperature for 5 minutes to finish cooking.

Run a small sharp knife around the edge of the cups.

Tilt the cups and slide the bacon, polenta, and egg onto plates and serve.