Peel the potatoes and cut them into medium chunks. Place them in a large pot with the eggs and cover with water. Boil until the potatoes are just fork-tender.
Drain the water right away and let the potatoes and eggs cool for a few minutes. They should be warm, not hot.
Cut the potatoes into small pieces without mashing. Chop the eggs gently to keep them neat.
Add the peas and carrots to a large bowl, followed by the onion, bell pepper, and celery if using.
In a small bowl, mix the mayonnaise, mustard, milk, salt, and black pepper until smooth.
Add the potatoes and eggs to the bowl with the vegetables. Pour the dressing over the top and fold gently until coated. Do not stir hard.
Cover and chill for at least 30 minutes before serving so the salad can set and the flavors can blend.