In a skillet over medium heat, add olive oil. Once hot, add the chopped onions and garlic, sautéing until translucent, about 2-3 minutes.
Add the thinly sliced beef to the skillet, cooking until browned. This should take about 5-7 minutes.
Stir in the sliced mushrooms and cook until soft, approximately 4-5 minutes.
Pour in the beef broth, Worcestershire sauce, and Dijon mustard, stirring well. Allow it to simmer for about 10 minutes until the sauce thickens slightly.
Remove the skillet from heat and mix in the sour cream. Season with salt and pepper to taste.
Preheat your oven to 400°F (200°C).
In a mixing bowl, whisk together eggs, milk, and a pinch of salt and pepper.
Dip each slice of French bread into the egg mixture, allowing them to soak briefly.
In a separate skillet, melt the butter over medium heat. Add the soaked French bread slices and cook until golden brown on both sides, about 2-3 minutes each side.
Transfer the toasted French bread to a baking sheet and place in the oven for about 5 minutes to warm through.
To serve, place each slice of French bread on a plate, spoon a generous portion of the beef stroganoff mixture over the top, and garnish with chopped parsley.