Bring 6 quarts water to a boil in a saucepan. Add 1/2 teaspoon salt and pasta; cook 5 minutes. Add broccoli; cook 3 minutes or until pasta is al dente. Drain through a sieve over a bowl, reserving 1/2 cup pasta water.
Melt butter in a Dutch oven over medium-high heat. Add onion and mushrooms to pan; sauté 5 minutes, stirring occasionally. Add garlic, and sauté 1 minute, stirring constantly. Add 1/2 teaspoon salt, shrimp, and carrot; sauté for 3 minutes, stirring occasionally. Add pasta mixture, 1/2 cup pasta water, cream cheese, and pepper to pan; cook for 3 minutes or until cheese melts and shrimp are done, stirring occasionally.
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