Place the cleaned artichokes in a large pot filled with water. Squeeze the juice of one lemon into the water to keep the artichokes from discoloring.
2. Bring a small saucepan of generously salted water to a boil. Add the artichokes and cook 10 minutes, or until tender. Drain, separate the leaves, then thinly slice the hearts. Set aside until ready to use.
3. Bring a large pot of generously salted water to a boil. Add the linguine and cook until al dente. Drain, reserving 1 cup of pasta water.
4. Zest two of the lemons into the large heavy-bottomed pot. Add the heavy cream and bring to a low simmer over medium-low. Whisk in the butter, 1 tablespoon at a time, until the sauce is emulsified. Add 1 cup pasta water and return to medium heat. Add the cooked linguine and the parmesan cheese and toss to combine. Remove from the heat, stir in the reserved artichokes, squeeze in the juice of two lemons, and season with salt and pepper. Serve hot, with the remaining parmesan cheese. Zest your last lemon over the top of each bowl before serving.
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