Pull off the outermost leaves of the artichokes until you get down to the lighter yellow leaves. Then, using a serrated knife, cut off the top third or so of the artichokes and trim the very bottom of the stem. Peel the stem, using either a paring knife or a y-peeler to remove the entire tough green exterior. Cut the artichokes in half lengthwise. With a spoon or melon baller, scoop out and discard the hairy choke and thorny inner leaves. As you work, rub the lemon half over the cut surface.
Heat the peanut oil in a pan, make it hot; slice artichokes very thinly and fry them for a few seconds until golden and crispy. Drain on paper towels. (If you act quickly, you don’t need to put artichokes slices in lemony water, and to pat them dry. Just slice and fry to obtain perfect crunchy dry fried artichokes).
Cook the Tortelloni according to package instructions and drain. In the meantime, heat 5 tbsp extra virgin olive oil and garlic in a large skillet over medium-high heat. When fragrant, add pasta to the pan and toss to coat. Discard garlic, divide among 2 plates, garnish with the fried artichokes and serve.