Cook the chicken. Preheat a 12-inch cast iron skillet over medium heat. Drizzle the pan with the olive oil and add the chicken thighs. 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.
Cook the vegetables and chicken stock. Add the carrots, celery, and onions to the hot skillet. 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 any cooked on flavor.
Add the chicken and remaining vegetables to the skillet. 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.
Preheat the grill or oven. Turn on your oven (or preheat your grill for indirect grilling) to 400 degrees F.
Mix the cheddar biscuit dough. Add the flour, baking powder, sugar and salt to 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.
Top the chicken pot pie with cheddar biscuit dough. 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 them in 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.
Bake the skillet chicken pot pie. 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.
Make the garlic butter. While the pie bakes, make the garlic butter. Combine the melted butter, garlic salt, and parsley in a small bowl and set aside.
Remove the baked pot pie from the oven or grill. Use a basting brush to paint the tops of the golden baked biscuits with the garlic butter mixture. Serve the pot pie warm.