Combine pork with 1 1/2 c. BBQ sauce in medium saucepan, bring to a simmer over low heat and cook until heated through, about 10 minutes.
Meanwhile, combine black beans, the remaining 1/2 c. BBQ sauce, splash of water, salt and pepper in medium saucepan. Bring to a simmer and cook until heated through, about 5 minutes.
Melt the butter in large nonstick skillet over medium heat, crack the eggs into the pan, season the tops with salt and pepper and cook until the whites are milky white and the yolks are slightly firm, about 4 minutes.
Scatter chips on a platter and scatter half of the cheeses over the top. Spoon on the hot pork and beans and top with remaining cheese. Slide the eggs in a single layer on top and sprinkle with garnishes of your choice (cilantro, pickled onions, Chiles, etc.)
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