Halve the leeks lengthwise and cut into 1-inch pieces. Halve the artichokes lengthwise. Heat the olive oil in a large skillet over medium-low heat, add the leeks, and cook until soft but not browned, stirring frequently, about 5 minutes. Remove the leeks from skillet and set aside. Increase heat to medium and add the artichokes. Cook about 3 minutes per side. Return the leeks to skillet and toss to mix. Stir in the lemon juice, salt, and pepper. Cook the linguine according to the package directions, reserving ½ cup of the pasta water. Transfer to a large bowl. Add the vegetables to the linguine and toss with half the Parmesan. Add some of the pasta water to moisten, if necessary. Sprinkle with the remaining cheese.
Easy and delicious, great pairing of ingredients and flavors.