Heat broiler, with rack in middle position. In a small saucepan, heat oil and garlic over medium-high until oil bubbles at edges. Add 1 teaspoon garlic oil to a large skillet and heat over medium-high. Season steak with salt and pepper and cook, in batches if necessary, until well browned and medium-rare, 5 to 7 minutes, flipping halfway through. Transfer to a cutting board, tent with foil, and let rest while preparing vegetables.
Return skillet to medium heat and add garlic slices and 2 teaspoons garlic oil. Add chard stems and cook, stirring occasionally, until crisp-tender, 3 minutes. Add leaves and season with salt and pepper. Cover, reduce heat to medium, and cook until leaves are wilted, 3 minutes. Meanwhile, brush bread with remaining garlic oil, season with salt and pepper, and broil until golden and crisp, 2 minutes. To serve, thinly slice steak against the grain and serve with chard and garlic bread.