Over high heat, bring a large pot of (salted) water to a boil. Add linguine and cook according to (al dente) package instructions, stirring occasionally to prevent the noodles from sticking together. After pasta is cooked, set aside ¾ cup of pasta water and drain the pasta.
Pat scallops dry with a paper towel (this will ensure a nice crust on the scallops). Season with salt and pepper. Add oil to a large skillet and heat over medium-high heat for a few minutes. Place scallops in pan, spaced out evenly. Sear for about 3-4 minutes on each side, or until a golden brown crust forms. Transfer scallops to a plate and cover with foil.
Using the same skillet, add butter and shallots, and cook over medium-low heat until translucent, around 5 minutes. Season with salt and pepper. Add garlic and cook for an additional minute.
Deglaze the pan by adding white wine and vegetable broth, scraping up any browned bits (this is where the flavor is!). Add heavy cream and bring to a simmer for around 3-4 minutes (the sauce will still be pretty thin, but will thicken up after pasta water is added).
Add cooked pasta to pan and toss with the sauce and ¼ cup of pasta water (this will help sauce stick to the noodles). Add more pasta water if needed.
Distribute pasta evenly over 4 plates and place scallops on top (divided evenly as well). Sprinkle fresh lemon juice and lemon zest over pasta, and garnish with fresh parsley.