Melt 1 tablespoon butter in a 5-quart Dutch oven over medium heat. Add garlic and red pepper and stir for 30 seconds without browning.
Pour in wine and simmer for 2 minutes. Add broth and salt and bring to a boil.
Stir in broken spaghetti and simmer uncovered for 8 to 10 minutes, stirring often to separate the strands. Add reserved water in small amounts if the noodles become dry before they are almost tender.
Fold in shrimp and simmer for 3 to 5 minutes, turning the shrimp through the sauce until opaque and 145°F, with tender spaghetti and a little liquid still flowing around it.
Remove from the heat and fold in the remaining 2 tablespoons butter, lemon juice, zest and chopped parsley. Toss until the sauce coats the strands and serve immediately.