Cut tomatoes into 1/2-inch slices, dredge in 1/4 cup flour.
Melt 1/4 cup butter in a large skillet over medium heat, add tomatoes, and cook until golden brown, turning once.
Arrange the tomatoes on a serving platter; sprinkle with salt, pepper, and brown sugar.
Melt remaining 2 tablespoons butter in pan drippings, add remaining 2 tablespoons flour, stirring until smooth.
Cook 1 minute, stirring constantly.
Gradually add milk, cook over medium heat, stirring constantly, until thickened.
Spoon over tomatoes.