If using frozen shrimp, place them in a colander and run under cool water until thawed.
Start boiling a salted pot of water for the fettuccine. Cook until al dente according to package instructions. Reserve 1 cup of pasta water.*
While the pasta cooks, add butter, Boursin cheese, heavy cream, chicken broth, and garlic to a skillet over medium heat.
Once the butter has melted and the pan is warm, stir to help the Boursin cheese melt into the sauce. This should take a few minutes.
When the Boursin has fully blended, let the sauce gently bubble for 2 minutes, stirring occasionally, until it thickens slightly.
Stir in the grated Parmesan cheese and cook for another minute.
Add the shrimp to the skillet and cook for 4 minutes, stirring occasionally, until the shrimp are pink and cooked through.
Season with salt and pepper to taste. Toss with the drained pasta and serve immediately.