Bring a pot of water (with a generous amount of salt) to a boil.
Add 1 Tablespoon of butter to a skillet and turn the heat to medium high. Melt the butter and add sliced mushrooms and a couple splashes of soy sauce. Cook the mushrooms for about 5 to 6 minutes, or until the liquid is cooked away and the mushrooms are cooked and browned. Remove the cooked mushrooms and set aside. Wipe the pan clean with a paper towel (if using stainless steel cookware, rinse with warm water being careful as you do it and then wipe dry).
Add the gnocchi to the pot of boiling water and set a timer (use the directions on the package) to ensure you don't overcook the gnoochi.
Prep the shrimp, pat dry with paper towels and season the shrimp with salt and pepper.
Add 2 Tablespoons of butter to the skillet and turn the heat to medium. Melt the butter and add the seasoned shrimp and garlic. Cook for 2 to 3 minutes, be sure to flip the shrimp too. Remove the shrimp and set aside.
Add the remaining butter and half of the green onions. Add heavy cream and cook for 2 minutes. Add cheese and the diced zucchini. Cook for 1 minute. Turn off the heat and add gnocchi and mix thoroughly. Add back the shrimp and the mushrooms. Mix again and serve with additional Parmesan cheese and green onions on top.