Cook the pasta according to the package directions. Drain, reserving 1 cup of the pasta cooking water.
Meanwhile, place the cream in a large saucepan. Add the garlic and set the pan over medium-low heat. Steep the garlic in the cream for 5 minutes. Note, we're not looking for bubbling cream here, just a few bubbles around the edges of the pan.
Add the artichokes to the cream with the marinade from the jar. Let steep for 5 more minutes (or until the pasta finishes cooking).
Add the pasta to the cream mixture and toss to combine. Fold in the parmesan cheese and spinach. Cook for 1 minute, until the spinach wilts. Add pasta water as needed to thin the sauce. Season to taste with salt and pepper.