In a skillet, cook the onion in the reserved fat over moderately low heat, stirring, until it is softened; let mixture cool. In a small bowl combine the onion mixture with the finely minced (do this in a food processor) bacon; season with freshly ground pepper. Into a bowl, sift together the flour, the baking powder, the baking soda, and the salt. Add the shortening and blend the mixture until it resembles coarse meal. Stir in the bacon mixture and the Cheddar; add the milk and stir the mixture until it just forms a soft sticky dough. Drop the dough by rounded tablespoons onto a buttered baking sheet. Bake the biscuits in the middle of a preheated 425 oven for 15 to 17 or until pale golden brown. Makes about 16 biscuits.