Preheat oven to 400 degrees Fahrenheit.
Peel and slice potatoes into 1/2-inch strips, placing in a medium-sized bowl of cold water as you cut to prevent oxidizing and browning.
Drain and pat potato strips dry with paper towels.
Pour vegetable oil to a depth of 3/4 inch into a large cast-iron skillet and heat until close to boiling.
Divide the potato strips into 3 batches and fry each batch separately; each batch should take about 10 to 12 minutes.
Remove strips with a slotted spoon and drain on paper towels.
When strips have cooled, cut into 1/4-inch dice.
Heat 2 tablespoons of oil in a clean, heavy medium-sized skillet; once oil begins to sizzle, add chopped onions, paprika, and salt.
Sauté over medium-high heat for 6 or 8 minutes, or until the onions start to soften and brown.
Clean cast-iron skillet and add butter; once melted, add potato strips and onions and mix well.
Sauté over medium-high heat until browned, then season with salt and pepper.
Transfer pan to preheated oven and roast for 10 to 15 minutes, or until crisp, and serve with steaks.