Blend flour + salt in processor. Add butter + shortening. Using on/off turns, process until mixture resembles coarse meal. Mix in enough ice water to form moist clumps. Gather dough into ball; flatten into disk. Wrap in plastic + chill until dough is firm enough to roll out, about 30 minutes.

Roll out dough on floured surface to 12-inch round. Transfer to 9-inch-diameter tart pan with removable bottom. Trim dough overhang to 1 inch. Fold overhang in + press, forming double-thick high-standing sides. Pierce crust all over with fork. Freeze crust 30 minutes. (Can be made 1 day ahead. Cover + keep frozen.)

Position rack in center of oven + preheat to 400°F. Bake crust until golden brown, piercing with fork if crust bubbles, about 20 minutes. Transfer crust to rack. Reduce temperature to 375°F.

Cook bacon in heavy medium skillet over medium-high heat until crisp, about 5-8 minutes. Using slotted spoon, transfer to paper towels + drain. Add shallots to same skillet + sauté until tender, about 4 minutes. Add arugula + sauté until just wilted, about 1 minute. Remove from heat. Add balsamic vinegar; toss to combine. Sprinkle arugula mixture, then bacon over crust.

Whisk cream, eggs, salt + pepper in large bowl to blend. Stir in cheese. Pour egg/cheese mixture into crust.

Bake quiche until filling is slightly puffed + golden, about 35 minutes. Let stand 10 minutes. Cut into wedges + serve.