In a large nonstick pot, combine the olive oil and unsalted butter. Turn the heat on medium-high, and let the butter melt.
Toss the meat with the flour, making sure to shake off the excess.
Once the butter has melted, add in your beef cubes, making sure not to crowd the pan.
Let the meat cook undisturbed for 3-4 minutes, then flip and brown the other side.
Let cook for a few minutes more, then add in the sliced onion. Season with salt, pepper, and garlic, and let cook for a couple of minutes.
Add in the mushrooms, season more if necessary, and saute for several minutes until the veggies have softened. Pour in the beef broth.
Add in the Dijon mustard, mix everything together, and add more seasonings if needed.
Cover, and cook over very low heat for 2-3 hours, until meat is very tender and falls apart.
Shortly before serving, stir in the sour cream... it will make your stroganoff extra creamy! Serve the beef stroganoff over plain noodles, rice, or mashed potatoes. Enjoy!
*NOTE: if you want to make this in the slow-cooker, just add everything to the crockpot at step 8 instead of leaving it on the stove. Cook on high for 4-5 hrs, low for 8-10 hrs *