Heat 1 tbsp butter & Italian seasoning over medium heat until butter starts to melt. Add in shrimp and toss until shrimp is cooked (turns orange). You can use precooked shrimp and just quickly heat with this step. Set shrimp aside.
In a large frying pan or wok add 1 tbsp butter, pasta, milk, water, salt, and pepper. Bring to a boil and reduce to medium / high to simmer, pasta should be al dente once water & milk have boiled out. Drain excess liquid if necessary (a little in the pan is fine).
Add pesto sauce, Parmesan, artichoke hearts, and cooked shrimp to the pan. Toss over low / medium heat until everything is evenly combined and warm.