In a large pot or Dutch oven, bring 3 quarts water and 1 tablespoon salt to a boil. Add pasta. Cook until al dente, about 7 to 10 minutes, adding the shrimp, broccoli, peas, bell pepper, and carrots to the pot during the last 4 minutes of cooking time. Drain well.
In the same pot, melt butter until foaming. Stir in garlic until fragrant, about 30 seconds. Add dill, onions, thyme, cream, broth, Parmesan, 1/2 teaspoon salt, and 1/2 teaspoon pepper.
Bring to boil, whisking constantly, then reduce heat to low and simmer 5 minutes. Add pasta, shrimp, and vegetables back to the pot and toss to combine. Season to taste with salt and pepper (I don't think it needs anymore at this point) and serve with additional parmesan cheese.