Soak potatoes in salted water for a few minutes then drain well; grate onion into potatoes. Heat oil in a skillet over medium-high heat with canola oil; add butter to oil and melt. Add potatoes and onions to the skillet, and season with salt, pepper, paprika and garlic. Cook hash browns until crispy and brown, turning occasionally.
Warm hot dogs in simmering water to heat through. Remove and split them open, cutting them lengthwise to open them up like books. Cook dogs on a hot griddle until casings and meat are crispy on both sides. Remove to toasted, buttered rolls. In the same skillet, fry eggs over-easy or medium.
Top dogs with mustard then potatoes; drizzle with ketchup, top with egg and dot with hot sauce. Serve.