Preheat a 12 inch cast iron skillet over medium heat. Drizzle the pan with the olive oil and brown the chicken thighs for 4-5 minutes per side, seasoning the thighs with salt and pepper. Remove to a cutting board, chop into bite sized pieces and set aside.
To the hot pan, add the carrots, celery, and onions. Cook for 6 minutes or until the vegetables are softened and the onions are translucent. Stir in the garlic and cook for 1-2 more minutes. Stir in the butter and sprinkle with the flour. Stir until there are no flour lumps and the vegetables are coated with the butter/flour mixture. Pour in the chicken stock while stirring quickly and scraping the bottom of the pan to release and cooked on flavor.
Stir in the cut up chicken thighs, peas, parsley, salt and pepper. Bring to a boil for 1-2 minutes and turn off the burner. Turn on your oven (or preheat your grill for indirect grilling) to 400 degrees F.
Add the flour, baking powder, sugar and salt in a large food processor and pulse several times to combine. Add in the butter and shortening and pulse 4-5 more times, or until the butter is the size of small peas. Add the cheese and pulse once or twice more until just incorporated. Pour in the milk and pulse until the dough just comes together.
Use your hands to grab a 1/4 cup portion of the biscuit dough. Flatten slightly and set gently on top of the chicken gravy mixture, being careful not to submerge the dough. Repeat until the dough is gone and the top of the skillet is covered with biscuit dough. As you near the end of the dough, break it into smaller pieces and fill in all of the small edges and empty spaces.
Transfer the skillet to the preheated oven or grill and bake for 25-30 minutes, or until the tops of the biscuits are golden and the pot pie is bubbling.
While the pie bakes, make the garlic butter. Combine the melted butter, garlic salt, and parsley. Use a basting brush to paint the tops of the golden baked biscuits with the garlic butter mixture and serve the pot pie warm.