Place the russet potatoes in a large pot and cover with cold water by about 2 inches. Bring to a boil and cook for 35-45 minutes until a fork easily pierces the largest potato. In a separate small pot, place eggs in cold water, bring to a boil, then remove from heat and let sit covered for 10 minutes.
While potatoes cook, finely dice the celery, onion, and green bell pepper into similar-sized pieces. Finely grate the carrot. Peel the cooled hard-boiled eggs and chop them into bite-sized pieces. Measure out the mayonnaise, mustard, salt, celery seed, and white pepper into a bowl and whisk together to create the dressing base.
Once potatoes are tender, drain and let cool just enough to handle. Remove the skins and cut into 1-inch cubes. Place the warm cubed potatoes in a large mixing bowl and sprinkle with 1 teaspoon of salt.
Add the prepared celery, onion, bell pepper, grated carrot, and chopped eggs to the salted potatoes. Pour the prepared dressing mixture over everything and fold gently until evenly coated.
Transfer the potato salad to a serving bowl and refrigerate for at least 1 hour before serving.
Just before serving, taste and adjust seasoning with additional salt, pepper, or a splash of mayo if needed.