Add the oil and butter to a skillet over medium-high heat. Once the pan is hot, add the mushrooms and onions. Sauté, stirring occasionally, for about 7-10 minutes or until the water has been released from the mushrooms and it cooks off and they get a nice sear. Remove the mushrooms/onions from the pan and set aside.
Add the ground beef to the skillet and cook it until browned (about 8 minutes), breaking it up with your spoon as you go along. Once the beef starts cooking a bit, stir in the garlic. If there's a lot of excess fat (there shouldn't be if you used very lean beef), spoon most of it out once the meat is done browning.
Sprinkle the flour over the beef and stir it in. Let it cook for about a minute (stir it a few times).
Add in the Worcestershire sauce, Dijon mustard, and broth, and cook for another 1-2 minutes, stirring until the flour & mustard have dissolved and it's heated through (also be sure to scrape the bits from the bottom of the pan). I like to add more Worcestershire sauce and Dijon mustard than suggested, but I left it fairly mild on purpose so you can easily build on the flavors if needed.
Add the mushrooms and onions back to the pan (stir them in).
Take the pan off the heat and stir in the sour cream. Season with salt & pepper as needed. Serve immediately over buttered egg noodles, mashed potatoes, or rice.