Mix flour, baking powder and salt in a large bowl. Cut in butter until crumbly. Stir in milk, adding just enough for the dough to come together. Knead by hand for one minute.
Divide the dough into 12 evenly-sized balls. Flatten the dough balls into a circle with your hands or with a rolling pin. Press into muffin tins and poke the bottoms of each one several times with a fork. Bake at 350 degrees for 5 minutes.
Meanwhile, cook ground beef in a large skillet. Season with salt. Drain.
Stir milk into ground beef in the pan and add shredded cheese. Continue cooking over low heat until cheese is melted and smooth. Stir in ketchup, mustard and relish.
Set aside some bacon to garnish the cups; stir the remaining into the beef and cheese sauce.
Spoon cheeseburger mixture into the biscuit cups. Garnish with bacon and additional shredded cheese, if desired. Bake for about 15 minutes, until biscuit cups are golden brown.