Whisk tarragon, 1/2 bunch mint, yogurt, 1 tablespoon olive oil, garlic, cumin, and 1 teaspoon black pepper together in a bowl; pour marinade into a resealable plastic bag. Add lamb steaks, coat with marinade, squeeze out excess air, and seal the bag. Marinate in the refrigerator, 8 hours to overnight.

Preheat an outdoor grill for high heat, and lightly oil the grate.

Whisk 1/4 cup olive oil, sherry vinegar, honey, salt, and pepper together in a bowl. Add 2 tablespoons chopped mint and stir to combine vinaigrette.

Remove steaks from marinade and scrape off all herbs and garlic; discard marinade. Drizzle steaks with 1 tablespoon olive oil and season with salt and pepper.

Cook steaks on the preheated grill until browned on the outside and slightly pink in the center, about 6 minutes per side. An instant-read thermometer inserted into the center should read 130 degrees F (54 degrees C). Transfer steaks to a plate, drizzle 1/2 of the vinaigrette over the steaks, cover the steaks with foil, and let rest for 10 minutes. Transfer steaks to individual plates and drizzle remaining vinaigrette over each.