How to Make It
In a small saucepan, cook half of the bacon and the onion in 1 tablespoon of the melted butter over moderate heat until the onion is golden, 5 to 6 minutes. Add the honey, mustard and vinegar and simmer until the sauce is thickened and slightly reduced, about 8 minutes. Season with salt and pepper.
Meanwhile, in a small skillet, cook the remaining bacon until crisp. Transfer to paper towels to drain and let cool. In a bowl, combine the paprika, brown sugar, onion powder, garlic powder and celery seeds with 1 teaspoon each of salt and pepper.
In a medium bowl, gently knead the pork with the crisp bacon and liquid smoke. Loosely form the meat into 4 patties about 3/4 inch thick and set them on a plate lined with plastic wrap. Sprinkle the spice mixture all over the burgers, patting to help it adhere. Brush the burgers and both sides of the bread with the remaining 3 tablespoons of butter.
Light a grill. When the fire is medium hot, brush the grate with oil. Grill the burgers for 12 minutes, turning once, until just cooked through. Move the burgers away from the heat and grill the bread on both sides until toasted, about 2 minutes.
Set the burgers on 4 of the toast slices and top with the cabbage and a generous spoonful of the honey-mustard sauce. Cover with the remaining toasted bread and serve right away, passing the extra sauce separately.