Heat olive oil in a large skillet over medium heat. Add mushrooms, onion, and red pepper and sauté for about 5 minutes until veggies begin to soften. Add garlic and sauté for another minute.
Add butter to the skillet and stir as the butter melts. Add flour to the skillet and stir to mix the flour into the butter.
Reduce the heat to medium/low and pour the half & half and milk into the skillet while constantly stirring so that no lumps form. Continue to cook while stirring until sauce starts to thicken, about 2-3 minutes. Add chicken broth while stirring constantly to combine all ingredients.
Add gnocchi and shrimp and stir to combine. Continue to cook until the shrimp are pink and opaque, about 3-5 minutes. Add fresh herbs, salt, pepper, and red pepper flakes. Stir in the parmesan cheese.