Heat about 3 tablespoons of olive oil in a large skillet on medium heat until almost ready to smoke.
Salt and pepper chicken breasts, place in skillet seasoned side down, and then season top side. I added a dash of smoked paprika for flavor.
Keep an eye on the chicken while you prep the vegetables and spices.
Cook about 10 minutes while you’re prepping the vegetables.
When first side of chicken is golden brown, flip with tongs.
Cook about 10 more minutes.
Get all your vegetables ready. Cut the carrots, celery, bell pepper, and onion into small pieces about 3/8″ square.
For the right texture, you want the chicken above 160° F, preferably closer to 165° F.
Take the chicken out of the skillet with tongs and place on paper towels to drain any excess frying oil. Cool at least 10 minutes.
Place each clove of garlic on the cutting board, place your chef’s knife on top, and whack it lightly with the heel of your hand, just enough to slightly crush it without breaking it up, and then remove the thin outer shell with your fingers.
Mince the garlic with a garlic press.
If you don’t have a garlic press, place the garlic under the chef’s knife again, but this time whack it hard enough to completely crush it. Then use the knife to mince it.
Pull the rosemary and sage leaves from the branches and finely chop.
Have all your vegetables and spices ready for the upcoming steps.
Use two dinner forks to shred the chicken. Basically, one fork anchors the chicken and the other fork shreds away from it.
Have your shredded chicken ready for the upcoming steps.
Heat a tablespoon or so of olive oil in a dutch oven. You need just enough to coat the vegetables.
Cook the vegetables on medium heat, stirring occasionally, for a few minutes until the onions are slightly translucent, and then add 1/4 cup butter and melt it.
Have your chicken broth and heavy cream ready for the upcoming steps.
When the onions are completely translucent and almost but not quite soft, add the garlic. Salt and pepper the vegetables to taste, and stir in 1/4 cup flour.
Notice that between the 1/4 cup of butter and the 1/4 cup of flour, we’ve added the elements of a roux, even though we haven’t explicitly made one. But, just like a roux, be sure you cook and stir it a few minutes, because nobody likes the taste of raw flour.
Add the chicken broth and stir until the sauce thickens.
You need to stir a lot during this phase to expose the different parts of the sauce to the heat of the pan as it thickens.
Stir the spices into the thickened sauce.
Stir the heavy cream into the thickened sauce, and keep stirring until the sauce has a smooth creamy texture.
Stir the cooked chicken into the sauce.
Let the completed filling cool while you roll out the top crust.
Preheat oven to 425° with shelf in middle or next lower position.
Get the dough for the top crust out of the refrigerator and let it come to room temperature.
Roll the top crust out just a little larger than the pie pan (so you can trim it.)
Dump the pan of cooled filling into the bottom crust and smooth it out with your spatula.
Sprinkle a layer of grated cheddar over the filling.
You can mix the cheddar into the filling if you prefer.
Use the wax paper as support as you gently fold the dough into fourths. Now pick it up by the folded corner and transfer it to one quadrant of the top of the pie, and then gently unfold it. Use excess dough to patch any rips or holes. Trim the edge of the dough to match the bottom crust, and then gently but firmly press the outer edge of the top crust onto the bottom crust and smooth into place.
Place one egg and one tablespoon of heavy cream (milk or half-and-half will do) in a container.
Beat the egg mixture with a dinner fork until smooth.
Use a brush to spread an even thin layer of the egg mixture over the top of the crust.
Poke the top of the pie gently with a fork about four times, leaving 16 holes. Be sure to poke near the middle of the pie so it won’t leak through the holes.
Bake 35 minutes until golden brown.
Remove the pie from the oven.
Cool on wire rack at least 15 minutes before serving.