Heat olive oil in a large skillet over medium-high heat. Season elk steak with salt and pepper, then add to hot skillet. Cook for 5-6 minutes per side, or until steak is cooked to desired doneness. Remove steak from skillet and set aside.
Melt butter in the same skillet. Add garlic and cook for 1 minute, or until fragrant. Pour in white wine and beef broth, stirring to combine. Simmer for 4-5 minutes, or until sauce reduces and thickens slightly.
Meanwhile, place potatoes in a large pot and cover with cold water. Bring to a boil and cook for 10-15 minutes, or until potatoes are tender. Drain potatoes and transfer to a large bowl. Mash with milk, sour cream, butter, and salt and pepper, until desired consistency is reached.
To serve, slice steak and divide between four plates. Top with sauce from skillet and serve with mashed potatoes.
Interesting Facts
Elk steak is a lean, flavorful meat that can be substituted for beef in many recipes.
Mashed potatoes are a classic American comfort food and are a perfect side dish for elk steak.
White wine and beef broth are added to the skillet to create a luxurious sauce for the steak.