Boil the red potatoes in a large pot until fork-tender, about 20–25 minutes. Drain and let cool.
Peel and chop the hard-boiled eggs into small pieces.
Cut the cooled potatoes into bite-sized chunks and place them in a mixing bowl.
Add the chopped eggs, mayonnaise, spicy brown mustard, salt, and black pepper to the bowl.
Gently mix everything together until well combined.
Taste and adjust seasoning if needed.
Refrigerate for at least an hour before serving for the best flavor.
Serve chilled and enjoy with your favorite main dish.