Halve 2 –2½ lbs Yukon Gold or red potatoes (or quarter if large) and place in a large saucepan and cover with water. Add 2 teaspoons salt to the water.
Place the saucepan on the stove over high heat and bring to a boil. Cook for 15–20 minutes, or until the potatoes are tender but not mushy. A paring knife should easily be able to pierce through the largest piece of potato in the pot.
Drain well and let the potatoes sit in the warm pot with the lid off for 10 minutes.
Remove the peels, and cut the potatoes into ½ inch pieces (or slightly smaller, depending on your preference).
Place the potatoes in a large bowl, and toss gently with 2 tablespoons vegetable oil, 1 tablespoon white vinegar, 1 teaspoon sugar, and ½ teaspoon salt. Let chill in the fridge for 2 hours. Leave it uncovered so any steam can escape.
Remove the potatoes from the fridge and stir in 1 cup mayonnaise, 2 teaspoons yellow mustard, ½ cup chopped yellow onion, ½ cup chopped celery, and 2 hard boiled eggs. Serve right away or refrigerate until ready to serve.
Top with paprika and/or additional slices of hard boiled eggs for garnish.
Notes
The salad will keep in the fridge for 4–5 days. I don't recommend freezing it as the dressing can get watery during the freeze/thaw process.Variations: add ½ cup chopped pickles (dill or sweet); ½ cup pickle relish; 2 tablespoons chopped fresh herbs like chives, parsley, or dill; or a small jar of drained and chopped pimentos. Serving tip: to take the salad to a warm-weather cookout, put it in a serving bowl, then nestle the serving bowl in a larger bowl filled with ice to keep it chilled (here's an example, but you can just make your own).