Preheat oven to 375 degrees and grease a baking dish. You can use a pie plate or 8-inch square baking pan. A cast iron pan works well too.
Melt butter over medium heat in a skillet. Set aside about 1 tablespoon of green onions for garnish. Add the shrimp and the remaining green onion to the pan and cook just until shrimp is about half way cooked. It will finish cooking in the oven.
Drizzle 1 tablespoon of hot sauce over shrimp mixture and set aside.
Place cream cheese, mayonnaise, and remaining hot sauce in a large bowl. Beat with an electric mixer until smooth.
Stir in the mozzarella cheese and cheddar cheese. Stir in shrimp mixture.
Transfer mixture to prepared baking dish. Bake for 20 minutes. Remove from oven and sprinkle with reserved green onions and the blue cheese. Return to oven for 5 minutes.