Place the sweet potatoes, red potatoes, and salt in a large saucepan and add water to cover by 1 inch. Bring to a boil over high heat, then reduce the heat to medium-low and simmer until the potatoes are just tender, about 8 minutes—a paring knife should slide in and out with very little resistance.

Drain the potatoes thoroughly and let them cool to room temperature, which should take 15 to 30 minutes. Once they are no longer steaming, combine the potatoes with the apples, arugula, and scallions in a large bowl.

Whisk the vinegar, mustard, honey, and hot sauce together in a small bowl. Drizzle in the oil slowly while whisking constantly to ensure the dressing emulsifies into a smooth, thick consistency.

Drizzle the dressing over the potato mixture and toss gently to coat so the arugula doesn't bruise and the potatoes keep their shape. Season with salt and pepper to taste and serve immediately while the greens are still crisp.