Prepare the horseradish dipping sauce by combining all ingredients together. Mix well. Refrigerate until serving.
In a large skillet over medium heat, add the butter, mushrooms and white onion. Cook for 10 minutes until the mushrooms and onion soften and the juices start to release.
Add the garlic, thyme, oregano, rosemary, salt and black pepper. Cook for 10-15 minutes, or until the mushrooms have released liquid and it has evaporated.
Add the white wine and balsamic vinegar. Cook down until all of the liquid is evaporated, about 10 minutes. Remove the mushrooms from the heat and let cool.
Preheat the oven to 400˚F.
Gently roll out the puff pastry sheets and divide each sheet into 9 small squares. Add a spoonful of mushroom filling to half of the squares, then cover the top with another square of puff pastry.
Gently press the top and bottom of each wellington together with a fork. Cut a slit in the top of each pastry, then brush with the egg.
Arrange the mini mushroom wellingtons onto a lined baking sheet and cook for 25 minutes. Let cool for 10 minutes. Serve with fresh rosemary, fresh thyme and horseradish dipping sauce.