Heat 1 tablespoon oil in a skillet over medium-high heat. Rub the steak with a slice of the garlic and season with ½ teaspoon salt and ¼ teaspoon pepper.
Cook the steak for 4 to 6 minutes per side for medium-rare. Transfer to a cutting board and let rest for at least 5 minutes before slicing.
Meanwhile, heat 2 tablespoons oil in a second skillet over medium-high heat. Add the bread and cook, tossing, until golden and crisp, 4 to 5 minutes. Transfer to a plate.
Add the remaining tablespoon of oil to the second skillet. Add the artichokes and cook, cut-side down, until lightly golden, 2 to 3 minutes.
Add the garlic, peppers, thyme, ¼ teaspoon salt, and 1/8 teaspoon pepper. Cook, tossing, until heated through, 1 to 2 minutes.
Add the bread and toss to combine. Serve with the steak.