Dice the onion. Heat a large pan, such as a Dutch oven, over medium-high heat. Add the olive oil. Let the oil heat for about 1-2 minutes. Add the diced onion to the pan and saute until the onions are lightly browned and translucent (about 3-5 minutes).
Add the ground beef to the pot with the onions. Brown the ground beef until it is fully cooked and no longer pink.
Empty the bag of frozen vegetables into the beef mixture. Let the vegetables cook until heated through. Alternatively, follow the package instructions to heat the frozen vegetables in the microwave before adding them to the pot.
Add the Worcestershire sauce and broth or water to the pot. Mix in the sour cream.
Turn the burner down to low. Top the beef mixture with prepared mashed potatoes. Sprinkle the mashed potatoes with the cheese before securing the lid. There should be enough heat to melt the cheese after about 10 minutes. Make sure that the beef and vegetables do not burn by making sure the burner is not too high and that there is just enough liquid at the bottom of the pan.