For the sweet tots: Preheat the oven to 375 degrees F.
Prick the sweet potatoes, then place them on a baking sheet and roast until the fork tender, about 1 hour.
Pour the oil into a Dutch oven and heat to 350 degrees F.
Peel and mash the sweet potatoes. Season with salt and pepper, and mix in 1 cup of potato chip crumbs. Place the remaining crumbs in a shallow bowl.
Place the whisked eggs and flour each in shallow bowls and season with salt and pepper. Roll the sweet potato mash into 1 1/2-inch tots.
Dredge the tots in the flour; dip in egg, letting the excess drip off; then roll in the chip crumbs to coat.
Fry the tots until golden brown, 1 to 2 minutes. Remove to a paper towel-lined baking sheet and sprinkle with salt. Keep warm until ready to serve.
For the honey mustard: Mix the mayonnaise, mustard, honey, vinegar and cayenne in a bowl until well blended. Serve with the tots.