Preheat oven to 450°.
Begin by searing your filet. In a large cast iron skillet, melt the butter over medium high heat. Season the filet pieces with salt and pepper. Sear on each side for 2-3 minutes, until a deep brown crust forms. You are just looking to put some color on the beef, not cook it through. Once the filet is seared, remove it from the pan and add to a bowl with the Dijon mustard. Toss to coat the filet in mustard and set aside.
While the filet is searing, prepare your mushroom mixture. This is commonly referred to as a 'Duxelles'. In the bowl of your food processor, add the mushrooms, shallot, garlic, and thyme. Pulse the mixture until it is finely minced.
Cook the mushroom mixture on medium high heat in the same skillet you seared the beef. The butter and rendered fat from the filet will help to break down the mushrooms. Cook the mixture for 10-15 minutes, until it has released all of it's moisture and is nicely browned. The mixture will have reduced by about ⅔. Lightly season with salt and pepper and set aside.
To assemble the wellington bites, place 1 piece of puff pastry into each hole of a muffin pan. Press lightly to form a cup. Spoon in some of the mushroom mixture, then top with a piece of prosciutto. Finish with a piece of filet and continue until the whole muffin pan is filled.
Bake wellington bites in preheated oven for 10-15 minutes, until the puff pastry is golden brown and puffed. Serve warm with Horseradish Cream.