Remove all the hard leaves and leaf tips from the artichokes. Peel the stem and cut back to about 5 cm (approximately 2 inches) in length. Cover immediately with the lemon juice and fill with water, to stop the artichokes from turning brown.
Mix in a bowl with olive oil, herbs, and garlic. Season with salt and pepper. Drain the artichokes and pat dry. Press until slightly flat so that the leaves open slightly. Cover with the herb oil and dust with the matze flour.
Heat the olive oil in a saucepan about 4 mm (approximately 1/8 inch) high. Cook over medium heat and place the artichokes in the oil. Cover and cook for about 25 minutes, turning a few times as needed. The artichokes should be soft and crisp. Serve with the lime wedges and basil leaves.