In a large pot or Dutch oven, bring 3 quarts water 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. Serve immediately, passing more Parmesan at the table for garnish.