Thaw puff pastry.
In a food processor, add the walnuts and quartered mushrooms. Pulse to combine.
Heat olive oil in a pan on medium heat. Add the walnut-mushroom mixture and the salt and pepper. Cook for 1-2 minutes, stirring, until you can smell the mushrooms.
Add the chopped onions to the walnut-mushroom mixture in the pan and stir. Cook another 3 minutes until the onions become fragrant and begin to turn translucent. Stir to prevent sticking.
Add the garlic, potatoes, and mixed vegetables. Stir to combine.
Next add the thyme leaves and vegetable broth. Stir. Place lid on pan and cook mixture for 10-15 minutes, until the broth is absorbed and a knife can easily pierce the potatoes. Stir frequently to prevent sticking. Taste and add more salt if desired. I find the bouillon base and 1/2 tsp of sea salt to be enough.
Set filling aside to cool. Preheat oven to 400°F. While the filling is cooling, roll out both sheets of puff pastry on a lightly floured surface. I rolled each into a 15" square. It does not have to be exact, but the more exact it is, the neater your finished hand pies will be.
Cut puff pastry into 16 squares.
Make your hand pies. Add 2 tablespoons of filling to one square of puff pastry and top with a second square. You may have to stretch it slightly to ensure it covers the filling and meets the edges of the other piece of pastry. Crimp the edges with a fork. Seal well to prevent them from coming apart in the oven.
Place hand pies on a parchment paper lined baking sheet. Bake for 15 minutes. The pastries will be golden brown and crispy.
Remove from oven and cool on a baking sheet. Enjoy!