A half-hour before cooking, remove the medallions from refrigerator.
Sauce: Put the shallots, garlic, vinegar, and all the herbs in a food processor and pulse until herbs are minced, with the motor running slowly drizzle in the olive oil until you have a thick sauce. Season with salt and pepper and the sauce is ready to serve.
Prepare a grill or a stove top grill pan with a medium-high heat fire.
Brush meat lightly with olive oil and season with salt and pepper. Place medallions on the grill and cook, without moving, until nice grill marks appear, about 4 minutes. Turn the medallions and continue to grill until an instant-read thermometer inserted into the medallions sideways registers about 120 degrees F, about 3 to 4 minutes more. Set aside on a cutting board to rest for 5 minutes before serving.
Divide medallions among plates and drizzle with some of the sauce. Serve. Pass the remaining sauce at the table.
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