Preheat oven to 400 degrees F. Lightly oil a baking sheet or coat with nonstick spray.
Place potatoes in a single layer onto the prepared baking sheet. Add olive oil, garlic, thyme, oregano, basil and Parmesan; season with salt and pepper, to taste. Gently toss to combine.
Place into oven and bake for 20-25 minutes, or until golden brown and crisp. Stir in butter until melted, about 1 minute.
Preheat oven to broil.
Season steaks with salt and pepper, to taste, and add to the baking sheet in a single layer.
Create 4 wells, gently cracking the eggs throughout and keeping the yolk intact.
Place into oven and broil until the egg whites have set and the steak is browned and charred at the edges, about 4-5 minutes per side for medium-rare, or until desired doneness.
Serve immediately with garlic butter, garnished with chives, if desired.