Gather all your ingredients before starting to ensure a smooth cooking process. Chop the onions, peel and chop the carrots, and cube the sirloin so everything is ready when you start cooking.
Preheat your oven to 375 F. In a large pan over medium-high heat, melt the butter with olive oil. Season the beef cubes with salt and pepper before adding them to the hot oil in the pan. Sear them until browned on all sides for about 6-8 minutes.
Once your beef is nicely browned, add in the chopped onions and carrots to cook alongside it for an additional 4-5 minutes until they start becoming tender. Sprinkle flour over this mixture and stir well to combine; let it heat for another 1-2 minutes.
Pour in both apple cider and beef broth into your pan, bringing everything to a boil while stirring occasionally. Once boiling, transfer this mixture into an oven-safe dish, cover it, and place it in your preheated oven to cook for about 1 – 1 ½ hours.
While your stew is baking, bring a pot of water to boil and add peeled potatoes cut into chunks until they are fork-tender. Drain them once cooked, return them to their pot, then mash together with milk, sour cream, shredded cheddar cheese, and chives until smooth.
After your stew has finished cooking, remove it from the oven and let it cool slightly before serving. Spoon generous portions of stew over fluffy mashed potatoes on each plate for a comforting meal that captures all those autumn flavors beautifully!