Prick pie shell with fork. Bake 6 to 8 min. or just until lightly browned. Remove from oven; set aside. Reduce oven temperature to 375 degrees F.
Cook and stir bacon in small skillet on medium heat until crisp. Remove bacon from skillet with slotted spoon; drain on paper towels. Discard all but 1 tablespoon drippings from skillet. Add broccoli and shallots to drippings; cook and stir 3 to 5 min. or until shallots are tender. Spoon into medium bowl. Add bacon; mix lightly.
Whisk eggs and milk until blended. Add to broccoli mixture with 3/4 cup cheese; stir. Pour into pie shell; top with remaining cheese.
Bake 35 min. or until knife inserted in centre comes out clean.