Bring a large pot of salted water to a rolling boil. Add the linguine and cook until al dente, approximately 7-9 minutes. Reserve 1/2 cup of the pasta water and set aside. Drain the linguine without rinsing.
Immediately transfer pasta to a large bowl, and add 1 1/2 tablespoons reserved oil from the artichokes jar along with the spinach. Use tongs to toss the ingredients together, allowing the heat from the pasta to slightly wilt the spinach.
Once the spinach has wilted, toss in the artichokes, mozzarella, parmesan, and black pepper. Add the reserved pasta water as needed to keep the linguine from becoming sticky as the cheese absorbs the moisture.
Taste for seasoning; add additional oil from the artichokes jar if desired.