In a large pot, combine the cardoons and lemon juice and add water to cover. Bring to a boil and cook until the cardoons are tender and easily pierced with the tip of a paring knife, about 45 minutes. Drain the cardoons and allow to cool. Slice into matchsticks and set aside.
Bring 6 quarts of water to a boil and add 2 tablespoons of salt. Cook bavette to al dente, about 10 minutes.
Meanwhile, in a 12- to 14-inch sauté pan, heat the olive oil until almost smoking. Add the garlic and toast until light golden brown. Add the cardoons and toss over high heat. Drain the pasta, reserving ½ cup of the cooking water and add the pasta directly to the sauté pan. Toss over high heat to coat. Add some of the pasta water to “loosen” the sauce as necessary. Add the parsley, chili flakes, breadcrumbs and season aggressively with salt and pepper. Divide the pasta evenly among four warmed pasta bowls, sprinkle with Pecorino Romano and serve.