Preheat the broiler to high with a rack set 2-inches from the heat source.
Heat the oil in a large skillet over medium-high heat. Add half of the kielbasa rounds, cut-side down, and cook until browned, about 2 minutes. Flip and cook for 1 minute more. Transfer to a paper-towel-lined plate. Cook the remaining rounds until both sides are browned. Add to the plate. Reduce the heat to medium, add the onion, and cook, stirring, until soft and slightly browned, about 5 minutes.
Add the tomato paste, brown sugar, vinegar, and chipotle to the onion. Pour half a can of beans (including the bean liquid) into the skillet and mash with a fork until creamy. Then add the rest of the beans (including the bean liquid), the cooked kielbasa, 1/2 cup water, 1 teaspoon salt, and a few grinds of pepper. Simmer until thick and creamy, about 20 minutes.
Toss the hot dog bun cubes with the melted butter on a baking sheet and sprinkle with salt and pepper. Broil until toasted and browned, flipping occasionally, about 2 minutes.
Divide the kielbasa and beans among 4 bowls. Top evenly with the hot dog bun croutons and pickle relish.
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