1. In 12-inch skillet over medium-low heat, cook bacon until browned but not crisp. With slotted spoon, remove bacon to paper towels to drain; reserve drippings.
2. Preheat oven to 450°F. Into medium-sized bowl, measure flour, baking powder, and salt. With pastry blender or 2 knives used scissors fashion, cut in shortening until mixture resembles coarse crumbs. With fork, stir in milk and bacon until mixture forms soft dough and leaves side of bowl.
3. On lightly floured surface, knead dough 10 strokes. Pat dough into a 1/2-inch-thick round. With floured 3 1/2-inch round fluted cookie cutter, cut out 4 biscuits, rerolling trimmings.
4. In cup, beat 1 egg; brush biscuits with egg. Bake on ungreased cookie sheet 10 to 12 minutes until golden; remove from oven. Cut biscuits horizontally in half; set top halves of biscuits aside. On bottom half of each biscuit on cookie sheet, place a cheese slice, folding cheese to fit if necessary, then a tomato slice. Bake until cheese melts; keep warm.
5. Into drippings in skillet over medium-low heat, break remaining eggs, one at a time. Cook eggs, basting with drippings, until whites are cooked and yolks are of desired firmness. With pancake turner, remove eggs from skillet, placing each on a cheese-topped biscuit half. Replace biscuit tops. Garnish with parsley.