Taste and adjust seasoning with a little more salt or pepper if needed. If the sauce feels too thick, you can splash in a bit of hot water or extra broth and stir until creamy.
Turn the slow cooker to WARM. Let the pasta sit for 5–10 minutes so the sauce thickens slightly and clings to the linguine.
Just before serving, sprinkle with chopped fresh parsley if you like, then twirl the linguine onto plates, topping each portion with plenty of shrimp and extra sauce from the bottom of the slow cooker.
For picky eaters, you can cut the red pepper flakes entirely and go a little lighter on the garlic; the butter and Parmesan still give plenty of flavor. If your family loves extra saucy pasta, add up to 1/2 cup more chicken broth at the beginning and an extra 1/4 cup Parmesan at the end. To sneak in veggies, stir in a couple of handfuls of baby spinach or frozen peas during the last 10 minutes of cooking; they’ll wilt and blend right into the pasta. You can swap the chicken broth for vegetable broth if you prefer, or use salted butter and reduce the added salt. If you only have spaghetti or fettuccine on hand, those will work in place of linguine; just keep an eye on the pasta and add a splash more broth if it looks dry. For a slightly richer, restaurant-style version, stir in 1/4 cup heavy cream or half-and-half along with the Parmesan. Leftovers reheat best with a spoonful of water or broth added before warming so the sauce loosens back up. And if someone in the house isn’t a seafood fan, you can cook a little chicken on the side and toss their portion of pasta with that instead of shrimp, using the same buttery garlic sauce from the slow cooker.