Whisk minced garlic, olive oil, salt, and black pepper in a bowl, then pour into a resealable plastic bag. Add the steaks, coat with the marinade, squeeze out excess air, and seal the bag. Marinate in the refrigerator for 8 hours or overnight.
Combine 12 garlic cloves and 1 cup olive oil in a small saucepan over low heat. Cook, stirring occasionally, until garlic is golden and tender, about 30 minutes. Set aside.
Preheat an outdoor grill for high heat, and lightly oil the grate. Remove steaks from bag, wiping off excess marinade with paper towels. Generously season steaks with salt and black pepper.
Cook the steaks on the prepared grill until they start to firm and are reddish-pink and juicy in the center, about 5 minutes per side. An instant-read thermometer inserted into the center should read 130 degrees F (54 degrees C). Remove steaks to a plate and let rest for 5 minutes.
Drizzle balsamic vinegar over steaks, then spoon a few cloves of oil-roasted garlic on top.