Put 1/2 cup of Minced garlic into a mortar and pestal. Drizzle some of the 1/4 cup of Olive oil over the garlic and crush up the garlic in the oil. Then stir in the rest of the oil and add a pinch of red pepper flakes. Pour mixture over shrimp and toss well. Refrigerate while you continue on.
Cut broccoli crown down to small flowerettes. Chop Onion into decent sized pieces. Slice mushrooms (Or open can and drain if you must).
Melt a stick of butter in a large saute pan over med-high heat. Add 2 TBSP of minced garlic, onions, and mushrooms. Add oregano. Saute until onions wilt. Add shrimp & garlic mixture and saute until shrimp turns pink. Add Wine and bring to a simmer. Add cornstarch and water mixture to thicken the sauce. Stir well. Turn down heat to low and add broccoli. Cover for 2 minutes. Stir well.