Combine the pork with 1 1/2 cups of the BBQ sauce in a medium saucepan, bring to a simmer over low heat and cook until heated through, about 10 minutes.
Meanwhile, combine the black beans, the remaining 1/2 cup BBQ sauce, a splash of water and some salt and pepper in a medium saucepan. Bring to a simmer and cook until heated through, about 5 minutes.
Melt the butter in a 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 the chips on a platter and scatter half of the Cheddar and Monterey jack over the top. Now spoon on the hot pork and beans and top with the remaining cheese. Sprinkle the cilantro and green onions over the top. Slide the eggs in a single layer on top and sprinkle with the pickled onions. Cut into wedges and serve.