Place flour and salt in food processor. Pulse to combine. Add butter and shortening. Pulse until texture of coarse meal.
With on-and-off pulses, add 4 tablespoons water just until mixture comes together. Pinch small handful of dough together; if it doesnt stick together, add another tablespoon water and process until combined. Scrape onto waxed paper; flatten into 5-inch disk. Chill 30 minutes.
Roll disk between floured sheets of waxed paper to 13-inch round, scant 1/4 inch thick. Place in 9-1/2-inch tart pan with removable bottom; trim excess dough, leaving 1/2-inch overhang. Fold excess dough over against sides. (If dough is too soft, refrigerate 20 minutes or freeze 10 minutes.) Refrigerate trimmed dough for other uses. Prick tart bottom all over with fork. Line crust with foil; fill with weights or dried beans.
Bake in 400°F oven for 20 minutes or until very lightly colored. Remove pan to wire rack; remove foil with weights. Reduce oven temperature to 350°F.
Place garlic in food processor. Whirl until finely chopped. With processor slicing blade, slice onions thin (press lightly on onion in feed tube).
Cook bacon in large skillet over medium heat. Remove bacon with slotted spoon to paper toweling to drain. Pour off all but 1 tablespoon bacon fat from skillet.
Add oil to skillet. Heat over medium heat. Add onions and garlic; sauté 15 minutes or until softened and golden; stir more frequently toward end of cooking time.
Slice mushrooms in processor with slicing blade. Add mushrooms, rosemary, salt and pepper to skillet; cook 10 minutes or until mushrooms are tender and onions are golden brown. Remove from heat. Chop bacon; stir into onion mixture.
Combine cheeses in bowl. Sprinkle half of cheese into tart shell. Spoon onion mixture over top. Sprinkle with remaining cheese.
Bake in 350°F oven 25 minutes or until cheese is golden. Serve hot or at room temperature, garnishing with fresh rosemary if desired.