In medium bowl, beat 1 of the eggs. Add rice. Stir until well blended. Press mixture onto bottom and up sides of lightly greased 9-inch pie plate or shallow baking dish. Set aside.
In non-stick skillet, over medium heat, add broccoli, pepper, onions and garlic. Cover. Cook, stirring occasionally, until broccoli is thawed, about 5 minutes. Set aside to cool slightly. Stir in cheese, pimientos and mushrooms. Spoon into prepared crust.
In large bowl, beat together remaining eggs and milk until well blended. Pour over vegetables.
Bake in preheated 375ºF oven until knife inserted near center comes out clean, about 35 to 45 minutes.