Preheat oven to 375F. Lightly oil a 9-inch loaf pan and set aside. In a large skillet, heat the oil over medium heat. Add the onion, celery, carrot and garlic. Cover and cook until softened, about 10 minutes. Remove from heat and set aside.
Place the three varieties of beans in a large bowl. Mash well, leaving some texture. Add the onion-carrot mixture, then stir in 1/4 c. of the ketchup, soy sauce, salt and pepper. Add the oats, bread crumbs, flour and parsley and mix until well combined. Scrape the mixture evenly into the prepared pan and smooth the top.
In a small bowl, combine the remaining 1/4 c. of ketchup with the mustard, sugar, vinegar and mix well. Spread the topping mixture on top of the loaf. Bake until firm, 50 to 60 minutes. If the top begins to brown too much, cover loosely with foil. Remove from the oven and set aside for 10 minutes on a wire rack before slicing.
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