Kosher or coarse salt and freshly ground black pepperto taste
Preheat the oven to 400°F. Whisk the eggs in a shallow bowl. Place the flour in another shallow bowl, and combine with the salt and pepper.
Preheat a large heavy skillet over high heat. While the skillet is heating, dip the lamb chops into the egg, and then dredge them in the flour mixture to coat the chops. Add the olive oil to the skillet, and when heated, brown the chops on both sides, about 3 minutes per side, working in batches if necessary.
If you can fit all of the chops back in the skillet in a single layer, do that, if not place them on a rimed baking sheet or in a roasting pan. Roast for about 7 to 10 minutes, until they reach an internal temperature of 130°F for medium rare. remove them from the oven and allow them to rest on a cutting board for about 5 minutes before serving - the internal temperature will climb a bit more.
While the chops are roasting, place the mint and basil leaves with the garlic in a food processor and process to mince. Add the olive oil, process again, then pulse in the Parmesan and the salt.