In a large pan, heat the butter and olive oil together over medium heat, and when the butter is melted completely add in the onion and carrot.  Saute until the onion is transluscent and the carrot is soft, about 5-8 minutes.  Add the garlic in and cook for another minute or two, until the garlic is fragrant.

Dump the flour in a little bit at a time, stirring after each addition to make a thick roux.  It will be a thick, lumpy mixture, but don’t worry!  The lumps will all smooth out.  Slowly pour the chicken stock in, beating quickly with the other hand to smooth out the mixture.  Pour in the milk and stir until the mixture is smooth, then add the salt, black pepper, rosemary, thyme, and lemon zest and juice.  Stir and continue to cook until the mixture has thickened to about the consistency of canned cream soup.

Remove from the heat and stir in the chicken and peas.  Preheat the oven to 425° and line a large baking sheet with a silpat mat or parchment paper.

To prepare the pastry, cut both sheets into 5″ squares by cutting it in half horizontally and then thirds vertically– you should have 12 squares.  Place about 1/3 cup of the chicken filling and a Tbsp. of parmesan cheese in the center of a square, leaving at least 1/2″ on each side.  Using a pastry brush, brush egg around the edge of the pastry, then lay another piece of dough on top of the filling and pinch the two squares of pastry dough together.  You may need to stretch the upper dough slightly, or you can roll it out to be slightly larger.  Then use a fork to press along the edges and seal them well.  If the fork is sticking to the dough, you can dip the tines in flour.  Repeat with the other squares of dough to make six hand pies.

Place the hand pies on the prepared baking sheet.  If the pastry dough is warm from sitting out and being handled, you should place it in the fridge for about 30 minutes to allow the butter in the pastry to re-harden.  When they are ready to bake, brush the top of each with more of the beaten egg, then use the tip of a sharp knife to score the pastry.  You can do it in any pattern you like, but be sure to not cut all the way through the dough so that it doesn’t burst and leak out the top.

Bake for 15 minutes, or until the dough has puffed, no longer looks doughy, and has begun to turn slightly golden.  Turn down the oven to 350° and continue to bake for 30-40 minutes, or until the tops are a deep golden brown, and lift with a spatula to make sure that the bottoms are a deep brown.

Remove from the oven and serve immediately.  If you had leftover filling, you may wish to serve it on the side to eat with the edges of thicker pastry.