Shred potatoes into a bowl of cold water. Let potatoes soak for at least 15 minutes, then pour them into a strainer and rinse. Dry potatoes in strainer with a clean kitchen towel by pressing against potatoes and removing as much moisture as possible.
Preheat waffle iron.
Toss shredded potatoes, butter, eggs, cheese, smoked paprika, salt, and pepper together in a bowl.
Pour mixture onto center of hot waffle iron and bake about 5 minutes.
Remove waffles carefully and top with sausage, scrambled eggs, and salsa. Serve immediately.