1. Wash and trim the cardoons. Cut into 2-inch lengths and drop into cold acidulated water.
2. Transfer the cardoons to a large pot of boiling, salted water and cook, uncovered, at a gentle bubble until tender. Drain in a colander. Shake to remove as much water as possible.
3. Heat the oil and butter in a large skillet until the butter is melted. Add the cardoons and stir over high heat until lightly golden. Distribute the garlic and lemon zest over the cardoons. Season with salt and pepper to taste and stir briefly over high heat. Sprinkle on the grated cheese and allow it to melt. Serve immediately.