Cook bacon in a 12-inch nonstick skillet over moderate heat, stirring, until crisp. Transfer with a slotted spoon to paper towels to drain, leaving fat in skillet. Peel potatoes and cut into 1/2-inch cubes. Cook in bacon fat over moderate heat, stirring occasionally, until golden and cooked through, about 15 minutes. Transfer with slotted spoon to paper towels to drain. While potatoes are cooking, combine shallot and vinegar in a large bowl and let stand 10 minutes. Stir in mustard and then olive oil until combined well. Just before serving, slowly fry eggs to desired doneness in vegetable oil with salt and pepper to taste in a large nonstick skillet over moderate heat. Add chicory to dressing, tossing to coat. Add bacon and potatoes, tossing, and season with salt and pepper. Serve salad topped with eggs.