Whisk together vinegar, mustard, 1/4 teaspoon salt, and 1/4 teaspoon pepper in a medium bowl. Whisk in the olive oil until combined. Fold in the crumbled blue cheese. Add the frisee and toss well to coat the frisee with the dressing. Season with more black pepper, to taste.
Heat a little of the butter in a small nonstick skillet over medium heat. Gently crack an egg into a small dish, and then add to the pan with the butter and cook until the white is set and the yellow is slightly firm, about 2 minutes. Season with salt and pepper and then gently turn the egg over and continue cooking for 1 minute. The yolk should still be slightly runny. Repeat with remaining butter and eggs.
Place the bread on a flat surface and top each with 1/4 of the frisee mixture, followed by 2 slices of prosciutto, and then an egg. Place a thin slice of blue cheese on top of the egg and garnish with ground black pepper. Place another piece of bread on top. Repeat to make a total of 4 sandwiches.