Heat the olive oil in a skillet over medium-high heat. Season the beef pieces with salt and pepper, then sear them for 1 minute per side until browned. Remove the beef and set it aside to cool.

In the same skillet, add the mushrooms, shallot, and thyme. Cook for 5 to 7 minutes until the mushrooms release their liquid and turn dry. Season with salt and pepper, then let the mixture cool completely.

Cut the puff pastry into 12 squares. Spread a thin layer of Dijon mustard on each beef piece.

Place one-third slice of prosciutto on each pastry square, followed by a spoonful of the cooled mushroom mixture and one piece of beef.

Fold the pastry around the filling and seal the edges. Place the parcels seam-side down on a baking sheet.

Brush the tops with the beaten egg. Bake at 400°F for 15 to 18 minutes until the pastry is golden and puffed.

Stir the sour cream and horseradish together in a small bowl. Serve the warm wellingtons with the horseradish cream on the side and chives sprinkled on top.