Thaw out the puff pastry sheets as you prepare your ingredients.
Liberally grease a 24-count mini muffin pan.
Place a large sheet of parchment paper on your work surface and roll each puff pastry sheet to make a large square. If the dough starts to stick, sprinkle a bit of flour over it.
Using a round 2 ½-inch cookie cutter, cut a circle from the dough and press it lightly into the prepared mini muffin pan. Repeat for a total of 24 circles of dough.
Brush the bottoms of the pastry cups with Dijon mustard and refrigerate them while you prepare the filling.
Preheat the oven to 425°F.
Place the mushrooms in the bowl of a food processor and pulse them until they are finely diced.
Melt 2 tablespoons of butter in a skillet over medium-high heat. When the butter starts to foam, add the mushrooms and fry until they release their liquid and begin to turn golden brown.
Add the prosciutto, garlic, thyme, and vermouth. Fry the mixture until the vermouth has been cooked down and the prosciutto has browned slightly but is still soft. Season with ½ teaspoon salt and ¼ teaspoon pepper.
Remove the skillet from the heat and stir in the remaining 1 tablespoon of butter until melted.
Transfer the mixture to a bowl and place it in the refrigerator for 10 minutes to cool.
Season the beef tenderloin with the remaining ½ teaspoon salt and ¼ teaspoon pepper.
Remove the muffin pan from the refrigerator and add a few pieces of the beef tenderloin to each pastry cup.
Spoon a teaspoon of the cooled mushroom mixture into each pastry cup, placing the mixture in and around the beef.
Bake the Beef Wellington Bites for 6 minutes at 425°F, then reduce the heat to 400°F and continue baking for an additional 6 minutes.
While the Beef Wellington Bites are baking, make the horseradish cream by combining the sour cream, mayonnaise, horseradish, and honey in a small bowl. Set aside.
Remove the muffin pan from the oven and run a thin knife around the edges of the Beef Wellington Bites to loosen them from the pan.
Dollop the tops of each Beef Wellington Bite with the horseradish cream. Place them on a platter and garnish with the rosemary.