Preheat a grill to medium-high. In a medium saucepan, heat half of the butter over medium heat. Whisk in the flour and cook, stirring, for 1 minute. Lower the heat to medium and slowly whisk in the milk until the mixture thickens and starts to boil. Stir in the cheese until smooth; season with salt and pepper. Cover to keep warm.
Thread the steak onto 4 skewers. Divide the bell pepper among 4 more skewers. Brush the pepper and beef with the oil and season with salt and pepper. Divide the bread among 4 more skewers and brush with the remaining butter. Arrange the bread and peppers on the grill and cook, turning, until charred on all sides, 5 to 7 minutes. Meanwhile, arrange the steak on the grill and cook, turning once, for about 3 minutes for medium. Serve the kebabs with the cheese sauce for dipping.