Add melted butter and minced garlic to slow cooker. Cook on LOW 15 minutes until fragrant.
Stir in chicken broth, seasonings (except fresh parsley), and half the Parmesan.
Cover and cook sauce on LOW 30 minutes to develop flavors.
Add cream and stir well. Add shrimp and lemon juice.
Cook on LOW 1-1.5 hours until shrimp are pink and cooked through.
Meanwhile, cook pasta according to package directions. Reserve 1/4 cup pasta water.
Add cooked pasta to slow cooker with remaining cheese and pasta water as needed.
Toss gently to combine. Let sit 5 minutes to thicken.
Garnish with parsley, extra cheese, and serve with lemon wedges.