In a large bowl, whisk to combine the mayonnaise, olive oil, vinegar, mustard, 1/2 tsp salt, and 1/4 tsp black pepper.
Place the cut up red potatoes into a large pot, and fill with enough cold water to cover the potatoes, plus an inch.
Bring the pot to a boil over high heat, and season with enough salt that it tastes like ocean water, about a couple tablespoons. Then cook the potatoes until fork tender. The time will really vary depending on if you sliced the potatoes or cut them into chunks, and how large, but for me it usually only takes about 5 minutes once the water is boiling, about 10-15 minutes total.
Once the potatoes are fork tender, drain them in a colander and let them sit for a few minutes for the excess steam to come off.
While the potatoes are still warm, toss them well with the dressing.
Stir in the celery, scallions, and chives, then serve warm or chill for several hours before serving. Enjoy!
Notes
Make-ahead instructions: You can make this ahead of time and store it in the fridge, but I recommend only making it up to 1 day ahead for peak freshness and flavor.Storing leftovers: Keep in the fridge for up to 4 days. Know that the flavor deteriorates a little more each day.