1. Preheat the oven to 450 degrees F.
2. Heat the butter in a large heavy skillet over medium-high heat until bubbly, then add the onion, carrot, celery, garlic, and season with 1 1/2 teaspoons kosher salt and 3/4 teaspoon pepper. Saute, stirring occasionally until vegetables are golden, about 10 minutes. Let cool.
3. Meanwhile, soak the breadcrumbs in milk until soft, about 5 minutes. Squeeze the bread to remove the excess milk and discard the milk.
4. Lightly beat the egg in a large bowl, then add in the cooled onion mixture, breadcrumbs and meatloaf mix. Gently mix until just combined. Form into 4 (4 1/2-inch) patties making a small indentation in the center of each.
5. Line a baking sheet with foil. Brush 1 tablespoon chili sauce on top of each patty, then place burgers on the prepared pan. Wrap each patty with 2 strips bacon, tucking bacon edges under the patties. Bake the burgers until an instant read thermometer inserted sideways into the burger registers 160 degrees F, 14 to 16 minutes. Alternately, preheat the broiler, remove the burgers from pan and broil about 4 inches from the heat source until the bacon browns, 2 to 3 minutes.
5. Place the burgers on the rolls and top with chili sauce and lettuce leaves, if desired.