In a small saucepan, melt 2 tbsp. butter over high heat. Whisk in the flour and cook over medium heat, whisking occasionally, for 2 minutes. Whisk in the milk, bring to a simmer and cook until thickened, about 5 minutes. Season with salt and pepper.
Position a rack in the upper third of the oven and preheat the broiler. Arrange 4 slices of bread on a parchment-lined baking sheet. Top each with one-quarter of the milk and sliced cheese. Spread one-quarter of the milk sauce over each sandwich; top with the remaining bread slices. Carefully spread the outsides of the sandwiches with the remaining 2 tbsp. butter. Broil, turning once, until the bread is lightly browned, about 3 minutes per side.
remove the baking sheet from the oven. Sprinkle the shredded cheese on top and broil the sandwiches again until the cheese is melted and lightly browned, 3 to 4 minutes. Meanwhile, drizzle the tomatoes with the sherry vinegar and EVOO; season with salt. Remove the sandwiches, slice in half and serve immediately with the tomatoes.