In a large, deep skillet, heat 1/4 cup plus 2 tablespoons of the oil until shimmering. Drain the artichokes and pat dry. Add the artichokes to the skillet and cook over high heat, stirring occasionally, until lightly browned in spots and barely tender, about 7 minutes. Add the garlic and cook, stirring, until lightly browned, about 2 minutes. Add the tomatoes and a generous pinch of salt and pepper and cook over low heat, smashing the tomatoes, until the artichokes are tender, about 5 minutes.