Preheat the grill to medium-high heat, about 400°F (200°C).
Pat the lamb chops dry with paper towels. Season both sides with 2 teaspoons kosher salt and 1 teaspoon black pepper.
Brush the lamb chops lightly with 1 tablespoon olive oil to prevent sticking.
In a food processor, combine parsley, cilantro, oregano, garlic, shallot, red pepper flakes, and red wine vinegar. Pulse until finely chopped but not pureed.
With the processor running, slowly drizzle in 1/2 cup extra-virgin olive oil until the mixture is well combined but still slightly chunky.
Transfer the chimichurri sauce to a bowl and season with 1/2 teaspoon kosher salt and 1/4 teaspoon black pepper. Stir to combine and set aside.
Place the lamb chops on the preheated grill. Grill for 4 to 5 minutes per side for medium-rare, or until desired doneness.
Remove the lamb chops from the grill and let them rest for 5 minutes.
Drizzle the remaining 1 tablespoon olive oil over the lamb chops.
Serve the grilled lamb chops topped with generous spoonfuls of chimichurri sauce.