Sear the Beef:
In a large skillet, heat olive oil and butter over medium-high heat. Season beef cubes with salt and pepper, then sear on all sides until browned (about 6–8 minutes).

Sauté the Veggies:
Add chopped onions and carrots to the pan. Cook for 4–5 minutes until softened and fragrant.

Add Flour:
Sprinkle in flour and stir well to coat the meat and veggies. Cook for 1 minute to eliminate the raw flour taste.

Deglaze and Simmer:
Pour in apple cider and beef broth. Scrape up the browned bits from the bottom of the pan. Bring to a boil, then transfer to a lidded oven-safe pan and bake at 375°F for 1 to 1½ hours.

Make the Cheddar Mash:
While the stew cooks, boil potatoes in salted water until fork-tender. Drain, return to the pot, and add milk, sour cream, cheddar, chives, salt, and pepper. Mash until creamy.

Serve:
Spoon mashed potatoes into a bowl or plate, ladle the stew over the top, and garnish with extra cheddar or chives if desired.