FOR SALAD: Cook bacon in a large nonstick skillet over medium heat, turning once, until crisp, about 6 to 7 minutes. Transfer with a slotted spoon to paper towels. Reserve 1 tablespoon of bacon drippings.
In a large bowl, combine romaine, endive, and chives; set aside.
In a food processor or blender, process bread to make crumbs; spread crumbs on a plate. Place goat cheese slices cut side down on work surface and press lightly to flatten. Dip each slice in egg; let excess drip off. Place on crumbs, pressing to coat evenly and completely.
Wipe out bacon skillet with a paper towel; add oil and heat over medium heat. Add goat-cheese patties and cook until browned, about 2 minutes per side (reduce heat if browning occurs too fast or cheese is melting). Transfer to a plate lined with paper towels. Remove skillet from heat.
DRESSING: Add reserved bacon drippings, olive oil, mustard and pepper to skillet. Whisk to combine. Add warm dressing and bacon to bowl with greens. Toss to combine. Arrange salad on individual serving plates and top each with a goat-cheese patty.