One Pan Shrimp Fettuccine Alfredo

3 tablespoons unsalted butter divided
16 ounces large shrimp peeled, deveined, and tails removed
2 cloves garlic minced
2 cups chicken broth
1 cup milk
8 ounces fettuccine noodles dry
1 cup Parmesan cheese grated
1/2 cup heavy cream