Prepare hot campfire coals or a grill or camp stove for medium heat.
Season the beef with ½ teaspoon each of salt and pepper. Toss the seasoned beef into a resealable bag and add the flour. Seal the bag and give it a good shake to evenly coat each piece with flour.
Set a Dutch oven over the coals or on the camp stove or grill and add the oil. When the oil is hot, but not smoking, add the beef and arrange it in a single layer on the bottom of the Dutch oven. Let it cook, turning occasionally, until golden brown all over, about 10 minutes.
Add the carrots, onions, celery, and garlic, and sauté until beginning to turn golden, about 5 minutes. Add the tomato paste and cook for 1 minute, stirring constantly.
Pour in the beef broth and bring the stew to a simmer, scraping the bottom of the Dutch oven to release any browned bits stuck to the bottom of the pot.
Stir in the potatoes and mushroom powder, if using. Cover the Dutch oven and simmer gently until the meat is very tender, adjusting the heat and adding more coals, as needed, about 2 hours.
Season to taste with salt and pepper, and serve hot.
Notes
Get ahead--To get ahead before heading out to camp, cube your stew meat and place it in a resealable bag. Peel your onions and dice your carrots and celery and store them in a separate container or bag in your cooler.
Watch the heat level--Avoid letting the stew boil vigorously as this can make the meat tough. You may need to move the Dutch oven to a cooler or warmer part of the fire throughout cooking in order to keep it at a gentle simmer.
Storage--Store leftover stew in an airtight container in your cooler or fridge for up to 3 days.
Reheating--Reheat in a Dutch oven over low heat until warmed through.