Place peeled & deveined shrimp in a medium sized bowl with 1 tbsp olive oil and lemon zest.
Heat olive oil in a large sauté pan over medium high heat. Add the garlic, onion, and white wine. Cook, stirring frequently, for 1-2 minutes until onions are translucent.
Stir in butter, chicken broth, and milk. Mix until the butter has melted. Bring to a boil, then add the spaghetti, tossing gently to coat in the broth mixture. Reduce heat to medium-low, cover and cook for about 8 minutes, stirring occasionally to make sure the noodles aren't sticking, until spaghetti just starts to get soft.
Add the shrimp, parsley, and red pepper flakes, toss to coat, cover and cook an additional 5-6 minutes, stirring occasionally, until the shrimp are fully cooked and the spaghetti is al dente.
Mix in the parmesan cheese and season with salt and pepper. If the mixture is too thick, add more broth until desired consistency is reached. To serve, divide between bowls and garnish with more parsley if desired.