In a large skillet, heat 2 tablespoons of olive oil and 1 tablespoon of unsalted butter over medium-high heat. Season 2 pounds of top sirloin beef with salt and pepper, then add the beef to the skillet. Sear for 2-3 minutes on each side until a rich brown color forms.

After the beef is seared, stir in 1 large chopped onion and 3 peeled and chopped carrots into the skillet. Cook for 4-5 minutes, stirring occasionally, until the vegetables are softened and fragrant.

Sprinkle 1-2 tablespoons of flour over the beef and vegetables in the skillet. Stir well for about 1 minute, allowing the flour to coat the ingredients.

Pour in 1½ cups of apple cider and 1½ cups of low-sodium beef broth while scraping the bottom of the pan. Bring the mixture to a boil, then transfer it to an oven-safe dish.

Cover the dish with a lid or aluminum foil and place it in a preheated oven set to 375°F (190°C). Bake for 1 to 1½ hours, until the beef is tender.

While the stew is baking, peel and chop 2 pounds of Yukon Gold or Russet potatoes. Cook in a pot of salted water until fork-tender (15-20 minutes). Drain and mash with ½ cup of whole milk, ½ cup of sour cream, 1 cup of cheddar cheese, and 2 chopped tablespoons of fresh chives.

To serve, spoon a generous portion of the creamy mashed potatoes into bowls, then ladle the hearty apple cider beef stew over the top.