Pat steaks dry with a paper towel. Rub garlic evenly over steaks; sprinkle with 1 teaspoon of the salt and ½ teaspoon of the black pepper. Let stand at room temperature 15 minutes.

Place a 12-inch cast-iron skillet on grill grates, and preheat grill to high (450°F to 500°F). Add 1 tablespoon of the oil to skillet; immediately add steaks to skillet. Cook until well browned, 4 to 5 minutes. Add butter to skillet, and flip steaks. Cook, tilting pan and constantly spooning butter mixture over steaks, until a thermometer inserted in thickest portion registers 125°F, 1 to 2 minutes. Remove from heat. Transfer to a cutting board, and let rest 10 minutes. Transfer skillet drippings to a small bowl; stir in parsley and thyme. Set aside. Slice steak; transfer to a serving platter.

Wipe skillet clean; return to grill over high heat. Add remaining 1 tablespoon oil to skillet. Add green beans and peppers; cook, stirring occasionally, until charred, about 4 minutes. Stir in onion and lemon juice, and cover and cook until vegetables are tender, about 2 minutes. Sprinkle with remaining 1/2 teaspoon salt and 1/4 teaspoon pepper. Arrange vegetables and steak on serving platter, and spoon parsley-thyme mixture over vegetables and steak.