Grate the zest from one lemon and then squeeze juice from both lemons into a small bowl; drain and cut the artichoke hearts into quarters and pat them dry with paper towels.
Bring a large pot of salted water to a boil (add 1 Tbsp salt), then cook 1 lb linguine according to package directions (about 8–10 minutes) until al dente; reserve 1 cup 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, 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 freshly ground black pepper; sauté 1–2 minutes per side until pink and opaque but not overcooked.
Add the quartered artichoke hearts to the pan and toss for about 2 minutes until heated through; remove the pan from the heat and stir in 1/4 cup chopped parsley, 1 tsp lemon zest, and 1/4 cup lemon juice.
Pour the shrimp and artichoke mixture over the drained linguine and toss to combine; if you prefer a looser sauce, add reserved pasta cooking liquid a little at a time (about 1/2 cup used as desired) until you reach the desired consistency.
Serve immediately with 1/2 cup freshly grated Parmesan cheese sprinkled on top.