Bring a large pot of water to a boil. Add the pasta with plenty of salt (about 1 tablespoon) and stir. Cook according to the package directions.
While the pasta is cooking, in a large deep skillet over medium heat, add the oil and butter. Once the butter is melted, add the shallot and garlic and cook, stirring, being careful not to burn, until the shallot is tender.
Add the artichokes, capers, lemon zest, and red pepper flakes and toss until the artichokes are well coated and slightly tender. Reduce heat to low while your pasta finishes.
Once your pasta is complete, reserve 1 cup of the pasta water and set aside. Drain the pasta and set aside.
Increase heat to medium-high, add wine and cook, stirring, until reduced by half, about 2 minutes.
Reduce heat to medium and add the pasta, salt, pepper and lemon juice and toss to coat in the white wine mixture. Once the pasta begins to absorb the sauce, add ⅔ cup of the pasta water and gently toss again to combine. Add the parsley and toss once more.
Divide the pasta among 4 plates and garnish with Parmigiano-Reggiano (if using) and additional parsley.