In a skillet, heat the olive oil and butter over medium heat. Add the diced onion and sauté for about 3-4 minutes until softened.
Add the minced garlic and sliced mushrooms to the skillet. Cook for another 5 minutes until the mushrooms are browned.
Increase the heat to medium-high and add the sliced beef. Season with salt, pepper, and paprika. Cook until the beef is browned on all sides, about 5-7 minutes.
Stir in the beef broth, Dijon mustard, and Worcestershire sauce. Bring to a simmer and let cook for about 10 minutes until the sauce thickens slightly.
Reduce the heat to low and stir in the sour cream until well combined. Allow it to heat through but do not boil.
While the sauce is finishing, preheat your oven to 375°F (190°C). In a mixing bowl, combine milk and a pinch of salt, then soak each slice of French bread in this mixture for about 1 minute on each side.
Place the soaked French bread on a baking sheet and bake in the oven for about 10 minutes, or until golden and crispy.
To serve, place a slice of the toasted French bread on a plate and spoon the beef stroganoff mixture over it. Garnish with fresh parsley.