Peel and cut 2 pounds of Russet or Yukon Gold potatoes into 1/2-inch cubes.
Peel and dice 2 medium carrots into 1/2-inch pieces.
Bring a large pot of salted water to a boil.
Add the potatoes and carrots and cook until tender but still firm, about 10–15 minutes.
In the last 2 minutes of cooking, add 1 cup of frozen green peas.
Drain all vegetables thoroughly and spread on a baking sheet to cool completely.
If using eggs, hard-boil 3 large eggs, then peel and chop.
In a large bowl, combine the cooled potatoes, carrots, peas, and chopped eggs (optional).
Stir in 1 cup of mayonnaise until vegetables are evenly coated.
Season with 1 teaspoon of salt and 1/2 teaspoon of black pepper; gently fold to combine.
Cover and refrigerate for at least 1 hour or overnight.
Before serving, stir again and adjust seasoning if needed.