Slice beef into thin strips. Cut red onion and pickled cucumbers into small cubes. Drain mushrooms.
Heat olive oil in a large pan over medium heat. Add beef strips and cook for 10-15 minutes, stirring occasionally. Season with salt and pepper. Increase heat to medium-high and cook for 1-2 minutes until lightly browned. Remove beef and set aside.
Add more olive oil to the pan. Cook onion cubes over medium heat for about 5 minutes, stirring occasionally, until translucent. Add cucumber cubes and mushrooms, cook for 3 minutes.
Stir in tomato paste and cook for 1-2 minutes. Pour in cream and crème fraîche, stirring well.
Add milk gradually, stirring, until the sauce reaches your desired thickness. Stir in mustard.
Return beef to the pan. Season with salt, pepper, and paprika. Reduce heat to low and simmer for 45 minutes.
Add white wine to taste if desired. Simmer for 2 more minutes. Taste and adjust seasonings.
Serve with boiled potatoes and sautéed mushrooms, or with rice.