Heat 1 tbsp. of the olive oil in a medium saucepan. Add the chopped onions and ground beef. Season with salt and pepper and sauté, breaking apart the beef as you do, until the beef is cooked through. About 5 minutes. Remove from the pan and set aside.
Add 1 more tbsp. of olive oil to the pan. Add the sliced mushrooms and sauté for 5 minutes until soft. Add in the minced garlic and sauté an additional minute.
Return the beef and onions to the pan with the mushrooms. Toss with the flour to coat evenly. Pour in the beef broth and bring to a boil. Simmer and stir constantly until the sauce thickens. About 5-7 minutes. Reduce the heat to low and stir in the heavy cream.
Serve warm over egg noodles or rice and garnish with chopped green onions if desired.