Preheat the oven to 400 degrees F and prepare the grill (or, alternatively, the steaks can be broiled or sauteed in a heavy pan or skillet using 1 tablespoon of hot olive oil or safflower oil; they will take approximately the same time to cook as they will on the grill).

To prepare the hash browns, peel and slice the potatoes into 1/2-inch strips. Place the strips in a bowl of cold water as they are cut to prevent them from oxidizing and browning. Drain and pat the potato strips dry. Pour the oil to a depth of 3/4 inch into a large, heavy cast-iron skillet and heat until close to boiling. Divide the potatoes into 3 batches and fry each batch separately; each batch should take about 10 to 12 minutes.

Remove the potatoes with a slotted spoon or strainer and drain on paper towels. When the potatoes have cooled, cut the strips into 1/4-inch dice.

Heat 2 tablespoons of oil in a clean heavy skillet. When the oil is hot and begins to sizzle, add the chopped onions, paprika, and salt. Saute over medium-high heat for 6 or 8 minutes, or until the onions start to soften and brown.

Melt the butter in a large ovenproof pan or skillet. Add the potatoes and onions, and mix together well. Saut? over medium-high heat until browned and then season with salt and pepper. Transfer the pan to the oven and roast for 10 to 15 minutes, until crisp.

Meanwhile, to prepare the steak, season the filets with salt and pepper. Grill for about 6 minutes per side for medium-rare or about 8 minutes per side for medium. Serve the steaks with the hash brown potatoes.