Cut rack of lamb into chops between each rib bone. Place lamb chops between pieces of plastic wrap and lightly pound with meat pounder to flatten to half the thickness. Remove from plastic, season with salt and pepper. Place the grated parmesan, the beaten egg and the breadcrumbs in three separate shallow bowls. Coat the lamb chops on both sides with the parmesan cheese. Then dip in the beaten egg and lastly coat with the breadcrumbs. Reserve.
To prepare the artichokes, trim the stem end and cut about a quarter of the top off the artichoke. Trim the outside leaves off with a paring knife until all that remains are pale green leaves. Trim the dark green portions off of the stem and base of the artichoke. Cut in half. Cut into quarters or sixths depending upon the size of the artichoke. If the artichokes are larger, it may be necessary trim out the center choke. Heat a skillet over high heat, add ¼ c. olive oil and sauté until the artichokes are tender and starting to lightly brown. Add the garlic, a tablespoon of lemon juice and a pinch of salt. Cook for a minute to soften the garlic. Remove from the heat and set aside to cool.
To assemble the salad, place the arugula in medium size bowl with the endive and artichokes. Dress with the remaining olive oil and lemon juices. Season with a pinch of salt and toss to evenly coat. Scatter shavings of the parmesan over top.
To serve, heat a wide-bottom skillet over high heat with the vegetable oil. Fry the lamb chops on each side until golden. Transfer to plate lined with paper towels to absorb any excess oil. Season with salt. Serve immediately with the salad on the side and a lemon wedge to season the chops.
Enjoy with a glass of Cakebread Cellars Cabernet Franc.