In a large skillet over medium heat, sauté the onion and garlic until translucent and fragrant, about 3-4 minutes.

Add mushrooms and thyme, cooking for another 5-7 minutes until the mushrooms release their moisture and become tender.

Season chicken breasts with salt and pepper. In the same skillet, cook chicken until golden brown on both sides, about 5 minutes per side. Remove and let cool slightly before shredding or chopping.

Mix the cooked chicken with the mushroom onion mixture, adding Dijon mustard. Allow to cool.

Roll out puff pastry on a lightly floured surface. Spoon chicken mixture in the center and fold the pastry over, crimping the edges to seal.

Brush the top with beaten egg.

Preheat oven to 375°F (190°C). Place the Chicken Wellington on a lined baking sheet and bake for 25-30 minutes or until the pastry is golden brown.

In a small saucepan, heat heavy cream over low heat to thicken, stirring occasionally. Add a pinch of salt and pepper to taste.

Slice the Wellington, drizzle with sauce, and serve.