Melt the butter in a large skillet set over medium heat. Once melted, add the flour to the skillet and whisk until evenly combined. Let cook for 60 seconds to cook off flour-y taste.
Whisk in the half and half, a little at a time, until evenly incorporated and the mixture's thickened.
Add the remaining sauce ingredients, and stir to combine. Continue stirring until the cheeses are completely melted & evenly combined. Remove the skillet from heat, and set aside. Reserve 2 tablespoons of cheese sauce, and set aside separately.
Divide the tortillas out into an even layer betwee two sheet pans. Spread half of the cheese sauce evenly out over one pan of chips, and then drizzle the other half evenly out over the other pan of tortilla chips.
Divide the meat, and then the black beans, between the two pans- spreading them out evenly over the chips.
Sprinkle half the shredded cheddar evenly out over one sheet pan, and the other half evenly out over the other. Drizzle the barbecue sauce evenly out between the two.
Bake the nachos at 350° for 4-5 minutes- just until the cheddar cheese has melted. Carefully remove the chips from the oven. Set aside.
To a cutting board or large flat serving platter, add the reserved cheese sauce to the center and spread it out into a thin circle. Set the prepared 'trash' can on top so that the cheese sauce is centered.
Use a spatula, or tongs, and layer the nachos in the trash can. Do this in three main layers, pressing down in between each one so they stick together well and also to maximize the amount that can fit. If you have a little leftover that's ok, but it will take more than you think to fill properly.
Once filled, top your trash can with garnishes- be careful not to touch or overlap the can edges, and pile them on.
Using two hands placed on either side of the metal can, carefully lift the can up and off the nacho tower. Set aside to clean and reuse another time.
Serve your warm nacho stack immediately.