Preheat oven to 400*. Drain and thoroughly rinse the canned artichokes. Cut each artichoke in half lengthwise, and lay cut side down on paper towels to dry. You want the artichokes to dry as much as possible before going into the oven. Let the artichokes continue to dry, changing the paper towels once, as you prepare the noodles.
For the noodles, I followed the method from gardenbetty.com, linked in the post above. I will describe what I did, but before making the noodles, I recommend studying the original post at gardenbetty.com.
In a large mixing bowl, measure two cups of all-purpose flour. Make a well in the center of the flour, crack three eggs and measure two tablespoons of olive oil into the well. Gently whisk the eggs and olive oil, incorporating a little flour into the well at a time, and continue whisking until the dough starts to come together. Dump the rough dough and any remaining flour in the bowl onto a clean, lightly floured surface and begin kneading the dough. Knead for about 10 minutes, or until dough is no longer sticky and the surface is smooth. Cover the dough with a towel and let rest on the counter for 30 minutes.
While the dough is resting, arrange the artichokes, cut side up on a parchment lined baking sheet. Drizzle lightly with olive oil and a pinch of salt. Roast in the oven for 45 minutes, or until browned and slightly crispy. When the artichokes are done roasting, turn the oven off, but keep them in the oven until you are ready to add them to the finished pasta.
To make the parsley pesto, in a food processor, combine the parsley, lemon juice, garlic cloves, olive oil, salt and pepper. Process for about 30 seconds, or until smooth. Set aside.
Before you roll out the noodles, put a large pot of salted water on to boil.
To roll out the noodles, cut the dough into quarters. On a well floured surface, using a rolling pin, roll out one segment of the dough at a time, as thin as you can get it. Mine took a lot of work but eventually got very thin. Once rolled out, sprinkle each side of the dough with flour. Fold the dough once in half and using a sharp knife, cut thin strips, to form the noodles. Once cut, unfold the noodles, gather together and sprinkle with flour to prevent sticking. Bunch the noodles, set aside and continue with the other segments of dough.
Once all noodles are cut, place the noodles in the salted, boiling water. After the noodles are added and the water returns to a boil, boil for 3-5 minutes, or until noodles are soft and tender. Taste one after three minutes to check if it is done. Cooking time will vary depending on the thickness of your noodle.
When noodles are done cooking, drain well and set aside. Return the pot to the stove and add the parsley pesto followed by the noodles, then toss well to combine. Add the artichokes and toss once again.
Serve pasta and top with freshly grated Parmesan cheese.