For the pickled red onions: Bring the vinegar, sugar, salt, peppercorns and 1 cup water to a simmer in a saucepan. Put the onion slices in a heatproof container and pour the hot vinegar mixture over them. Let sit for at least 1 hour before serving.
For the sweet potato tottine: In a deep fryer or large Dutch oven, heat the oil until a deep-fry thermometer inserted in the oil registers 375 degrees F.
Meanwhile, heat the beef stock in a saucepan until slightly simmering. In a separate small saucepan, melt the butter over medium-low heat. Once the bubbling subsides, add the garlic and cook until fragrant, about 30 seconds. Add in the flour while whisking vigorously to prevent clumps. Cook for 2 minutes. Slowly add in the hot stock while whisking. Bring to a simmer and season with salt and pepper.
Fry the tots in batches in the hot oil until golden brown, about 5 minutes. Remove and let drain on paper towels.
Add the tots to a bowl, place the cheese curds on top, cover in a ladleful of gravy and top with pickled red onions and fresh parsley.