Preheat oven to 350F. Lightly grease a muffin pan and set aside.
In a saucepan, heat 1 tbsp of olive oil over medium heat. Add the onions and carrots and cook for 3 minutes until soft. Set aside to cool.
In a mixing bowl, mix together the ground pork, thyme, nutmeg, sage, garlic, pepper and salt. Stir to combine. Add the cooked onions and carrots. Set aside.
To prepare the crust, heat the water and butter until it comes to a simmer over medium heat. In a bowl, stir the flour and salt together until combined. Add 3/4 of the hot water and stir. Stir until it forms a ball of dough. Add more water if needed. Knead until smooth. Set aside 1/4 of the dough in a warm area, covered, until needed.
Roll out the larger portion of dough on a lightly floured surface. Cut out rounds 1" larger than the muffin tin mold. These may vary in size depending on your pan. Press the pastry circles into pan. Fill each with some of the pork mixture. Lastly, roll out the second portion of dough and cut out circles for the tops of each pork pie. Seal the edges with your fingers or with a fork.
Brush the top of each pork pie with the lightly whisked egg. Bake for 45 minutes or until golden brown and cooked through. Let it cool before serving.