Set a 12-inch skillet on the stove over medium heat.

Add the bacon to the skillet. Cook it for 6 to 8 minutes, stirring now and then, until the pieces are browned and crisp.

Transfer the bacon to a plate with a spoon, leaving about 2 tablespoons of bacon fat in the skillet.

If the skillet looks nearly dry, add the olive oil to the bacon fat.

Put the onion into the skillet. Cook it for 2 to 3 minutes, stirring once or twice, until it starts to soften.

Add the Brussels sprouts and 1/4 teaspoon of the salt to the skillet. Cook for 4 minutes, stirring every minute or so, until the sprouts wilt and pick up some browned edges.

Add the apple and the black pepper. Cook for 3 to 4 minutes, stirring a few times, until the apple softens a little but still holds its shape.

Return about three-quarters of the bacon to the skillet and stir it into the vegetables.

Pour the apple cider vinegar and 1/4 cup water into the skillet. Stir for about 1 minute, until the liquid mostly cooks away and the vegetables look lightly glossy instead of dry.

Taste the vegetable mixture and add a little more salt if needed. Lower the heat to low.

Use the back of a spoon to make 6 small spaces in the vegetable mixture so the eggs have room to sit in the skillet.

Crack 1 egg into each space in the skillet.