In a medium saucepan over medium heat, bring the cola, ketchup, steak sauce, lemon juice and zest, and ginger to a simmer and cook, stirring occasionally, until reduced by half, about 20 minutes. Season to taste with salt and pepper.
In a small bowl, combine the butter and garlic. Preheat a grill or grill pan to medium heat. Spread the bread slices on both sides with the garlic butter and grill, turning once, until golden, about 5 minutes.
Brush the onion slices and steaks with olive oil and season with salt and pepper. Increase the heat to medium-high. Grill the steak and onions until the steak is cooked to the desired doneness (about 4 minutes on each side for medium-rare) and the onions are softened. Slice the steak into thin strips. Top each toast with steak, onions and cola sauce.