Bring a large pot of well-salted water to a boil over high heat.
Meanwhile, prepare the cardoons: Cut the base off the bunch to separate it into stalks, and discard any tough outer stalks or narrow leafy stalks from the center. With a paring knife, shave the stringy outer layer off each stalk. Cut the trimmed stalks crosswise into 1-inch pieces.
Cook the cardoons in the boiling water until tender, about 12 minutes. Drain well. (The cardoons can be prepared to this point up to 4 hours ahead.)
In a 10-inch skillet, melt the butter over medium-low heat. Add the garlic and cook over medium heat, pressing the cloves with a fork, until just beginning to color, about 2 minutes. Remove the garlic with the fork and discard.
Add the pepper flakes to the butter, wait about 15 seconds, and then add the cardoons. Cook, tossing, until heated through, about 1 minute. Toss with the Parmigiano, season to taste with salt and pepper, and serve.