Heat oven to 425°F. Make pie crust as directed on box for One-Crust Filled Pie using 9-inch glass pie plate. DO NOT PRICK CRUST. Bake 7 to 8 minutes or until crust begins to brown.
Meanwhile, in large bowl, beat eggs. Stir in milk, ham, rice and broccoli mixture, 1 cup of the Swiss cheese and the pepper until well blended.
Remove partially baked crust from oven. Reduce oven temperature to 400°F. Pour ham mixture into crust. Top with remaining 1 cup cheese.
Bake at 400°F for 15 minutes. Remove pie from oven; cover edge of crust with strips of foil to prevent excessive browning. Bake 20 to 25 minutes longer or until knife inserted in center comes out clean. Cool 10 minutes. To serve, cut into wedges.