Prepare a pot with salted boiling water and cook pasta according to package directions. Reserve about 1 cup of pasta water just in case you need it to thin the sauce.
Prepare the scallops using the tips from the post (pat them dry and don't sprinkle with salt and pepper till immediately before searing). I personally recommend not adding salt to the scallops as I find them naturally salty, but please season to your own taste.
Heat a large pan, non-stick or cast iron, with butter and oil over medium high heat. Once hot, add the dry scallops, keeping them at least 2 inches apart so they sear and don't steam. If they don't make a sizzle sound, your pan isn't hot enough. Leave them to sear for 2 minutes (don't move or touch them), or until a nice brown crust forms. Flip and cook another 2-2½ minutes or until you get the same crust on the opposite side. Set the scallops on a warm plate.
In the same pan, use the leftover butter/oil to saute the chopped shallot and garlic, about 2 minutes until softened and fragrant. If your pan is dry, use 1 tablespoon more butter or oil. Deglaze the pan by adding broth, scraping up any browned bits (this basically means add broth to a hot pan which should bubble up and start to simmer). Then add cream and bring to a simmer for about 3-4 minutes until the sauce has thickened. When you run a wood spoon through the sauce, it should leave a clear path.
Add cooked linguine and toss with the sauce, simmering to thicken it a bit more. If your sauce is too thick or isn't coating the pasta well, add in 1/4 cup of the reserved pasta water till it reaches your desired consistency. Add in fresh chopped parsley and kosher salt and pepper to taste. Top with the cooked scallops.
Notes
Use dry scallops instead of wet for the best sear/flavor. These will be a creamy, rosy pinkish color (not gray/white) and without sodium tripolyphosphate.
Scallops are naturally more salty. Salt them very lightly just before searing, or just season with a touch of pepper. You want that natural sweetness to shine.
The cream sauce here is very light to not overpower the scallops you spent so much money on! You can add a lemon wedge to each plate for some brightness and acidity. Or mix in some freshly grated parmesan with the pasta. These additions would not be HYH.
Use gluten free pasta for gluten free, and leave out the cream for a dairy free option. If you do this, I recommend adding fresh herbs like basil and chives for more flavor.