Pour 2 tablespoons of the oil in a skillet set over medium heat. Sauté the mushrooms with the shallots and thyme until all the moisture has evaporated and the mushrooms and shallots are cooked through, about 8-10 minutes. Set the pan aside to cool.
In the meantime, in another skillet, heat the remaining oil. Season the beef pieces with 1/2 teaspoon of salt and pepper. Place the beef in the heated skillet and sear on each side about 2-3 minutes, or until brown. Remove the beef from the skillet and set it aside.
When the mushrooms have cooled, place them into a bowl of a food processor and add the Parmesan cheese as well as the remaining salt and pepper. Process until the ingredients are combined and very finely chopped, but not pureed.
Divide the mixture and place it in the middle of eight of the puff pastry squares. Wrap a slice of prosciutto around the seared beef and place it on top of the mushroom mixture. Repeat with the remaining beef. Wrap the puff pastry around each piece of beef and pinch the seams together. Place each wellington, seam-side-down, onto an ungreased cookie baking sheet.
With the two remaining squares of puff pastry, use a small heart-shaped cookie cutter to make eight heart garnishes. Brush the surface of each pastry with the beaten egg and place a heart garnish on top. Brush the hearts with the beaten egg and refrigerate the wellingtons for 10 minutes.
Bake until the pastries become puffy and golden brown, about 10 minutes to achieve a medium-rare doneness. (Add 5 minutes to the baking time to achieve a medium doneness; 10 minutes for medium-well.) Let each wellington rest for 5 minutes before serving.
QVC is not responsible for the availability, content, security, policies, or practices of the above referenced third-party linked sites, nor liable for statements, claims, opinions, or representations contained therein. QVC's Privacy Statement does not apply to these third-party web sites.