Trim the green tops from the frisee, and trim the root ends. Separate the leaves and tear them into 2-inch pieces. Wash and spin dry in a salad spinner and divide the frisee into 4 shallow soup or pasta bowls.

Preheat a grill pan over medium-high heat.

Set a 10-inch saute pan over medium-low heat and add the bacon. Cook, stirring often until most of the fat has rendered, and the bacon is crispy, about 7 to 8 minutes. Dip bread slices in bacon fat just to coat and remove bread from pan. Place bread on grill pan and toast on both sides until golden.

Add the shallots to the bacon and cook, stirring until fragrant, about 1 1/2 to 2 minutes. Pour the vinegar into the pan and season with 1/4 teaspoon of the salt and 1/8 teaspoon of the pepper, remove from the heat. Use a slotted spoon to remove the bacon from the pan and drain onto a plate lined with paper towels. Drizzle the vinaigrette evenly over the lettuces, and divide the bacon among the bowls as well.

In a wide-mouthed saucepan, bring the water to a gentle boil with the white vinegar. Crack an egg into a cup, and gently slide it into the water. Slide each of the other 3 eggs into the water in the same manner. When the water comes back to a boil, reduce the heat to low and simmer until the eggs are set, about 3 to 3 1/2 minutes. Gently remove the eggs with a slotted spoon and pat dry with a linen cloth or paper towel. Place an egg over the top of each mound of frisee and season with the remaining salt and black pepper. Serve immediately.