Heat a grill to medium high. Whisk 2 tablespoons olive oil, 1 tablespoon balsamic vinegar, the mustard, thyme and 1 grated garlic clove in a bowl. Rub all over the steak and season with salt and pepper; set aside. Combine 2 tablespoons olive oil and the remaining grated garlic in a small bowl; set aside.
Toss the red onion and peppers with the remaining 2 tablespoons olive oil, 1 teaspoon salt and a few grinds of pepper. Grill the vegetables, flipping, until lightly charred and tender, about 5 minutes. Transfer to a bowl; stir in the remaining 2 tablespoons balsamic vinegar and the red pepper flakes. Cover with plastic wrap and set aside.
Brush the grill grates with olive oil. Grill the steak until browned, about 5 minutes per side for medium rare. Transfer to a cutting board and let rest. Meanwhile, toast the bread on the grill. Remove and cut into pieces; brush the cut sides with the garlic oil and season with salt and pepper.
Stir the mint into the pepper mixture. Thinly slice the steak against the grain. Serve with the peppers and garlic bread.