Heat your oven to 375 degrees.
Start by melting the butter in a skillet over medium heat. Once melted, add the mushrooms and season with salt and pepper. Saute the mushrooms for 4 minutes, then add the onion and carrot and cook for another 3 minutes.
Add the chicken stock, white wine, chicken, thyme, and tarragon. Let simmer for 5-7 minutes, until most of the liquid has been absorbed. Let cool while you prepare the pie crust.
Unroll the pie crusts, and use a bowl about 5 inches in diameter to cut two circles from each of the pie crusts. Roll out the remaining pie crust and cut a fifth circle. You might even have enough dough for a 6 hand pies - go for it!
Now it is time to assemble the hand pies. Start with a small handful of spinach, and then add about ¼ cup of the chicken filling. Top with a small handful of cheddar cheese.
Then carefully fold the dough in half. Press the edges together and fold them up, then use a fork to seal the edges. Repeat using all of the dough.
If you have a silpat, I recommend using it. Arrange the handpies on a pan and place then in the oven to bake.
After 20 minutes, remove the pies from the oven and brush them generously with olive oil. Then return then to the oven for another 5 minutes, or until golden brown.