Grate the zest from one lemon and then squeeze the juice from both lemons; set aside.
Drain the artichoke hearts well, quarter them, and pat dry with paper towels.
Bring a large pot of water to a boil, add 1 tablespoon salt, and cook 1 lb linguine 8–10 minutes or according to package directions until al dente. Reserve 1 cup of the pasta cooking liquid, then drain the pasta.
While the pasta cooks, heat a 12–14 inch heavy-bottomed skillet over medium heat and add 4 Tbsp butter and 3 Tbsp olive oil. When the butter is sizzling, add the minced garlic and cook, stirring, for about 1 minute until fragrant.
Add 1 lb peeled and deveined large shrimp in a single layer and season with 1 tsp sea salt and 1/4 tsp black pepper. Sauté 1–2 minutes per side until the shrimp turn pink and are no longer translucent.
Add the quartered artichoke hearts to the pan and toss to combine; cook 1–2 minutes more just until warmed through.
Remove the skillet from the heat and stir in 1/4 cup chopped fresh parsley, 1 tsp grated lemon zest, and 1/4 cup lemon juice.
Pour the shrimp and artichoke mixture over the drained linguine and toss to combine; add reserved pasta cooking liquid a little at a time (about 1/2 cup as desired) to loosen the sauce.
Serve topped with 1/2 cup freshly grated Parmesan cheese.