Saute diced onion, carrots and bell peppers until just tender over medium heat. Add ground meat and brown until done. Drain off fat in colander, wipe oil out of pan with paper towels. Return meat/veggie mix to pan over medium heat.
Add tomato paste, brown sugar, vinegar, paprika, chili powder, horseradish sauce and stir over heat until well mixed and spice scent blooms. Add tomato sauce PLUS one tomato can full of water. Cover and simmer over med-low for 30 minutes. If its too runny after that, remove cover and allow some of the juice to evaporate off before assembling.
Place parchment paper over two large cookie sheets and place 12 biscuits, evenly spaced on them. Press biscuits out until they are the size of small saucers (about 6 inches across).
Put 1/2 cup sloppy joe mix on each biscuit and some shredded cheese. Stretch remaining 12 biscuits to saucer size, place over sloppy joe's, crimp edges with fork to seal.
Bake at 350 degrees for 10 minutes. Melt butter while waiting (stovetop or microwave). Remove joe's after ten minutes, baste with melted butter and top with salt/pepper and more shredded cheese. Return to oven to finish cooking for add'l 3-5 minutes.