Preheat the oven to 425 degrees.
Then, heat a large skillet over medium-high heat. Add the butter and oil to the skillet. Next, add in the diced shallots, celery, and carrots and cook for about 5-7 minutes. Then, add the minced garlic,seasonings, and thyme. Sauté for an additional 1-2 minutes or until the shallots are translucent and the veggies have started to become tender.
Turn the heat to medium and sprinkle the flour over the veggies. Stir until well combined and cook for about 1 minute. This should create a thick paste.
Add the chicken broth, half and half, and lemon juice to the skillet. Stir or whisk until well combined, making sure to incorporate the flour well and any brown bits on the bottom of the skillet (that's flavor!). Bring the filling to a simmer and let simmer for 3-5 minutes until it has thickened. Cook longer for a thicker filling. Be sure to taste the pot pie to adjust seasonings.
Remove the skillet from the heat and stir in the chicken and the frozen peas until well combined.
Make your buttermilk biscuits. Note, you don't have to be precise here. You can simply cut the biscuits in squares for ease. Top the pot pie with the biscuits (7 around the edge of the pot pie and one in the middle). Use a pastry brush to brush the top of each biscuit with egg wash or buttermilk.
Bake at 425 degrees for 15-20 minutes, until the biscuits are golden brown and cooked through.
Remove the skillet from the oven and then brush the top of each biscuit with melted butter. Top with flaky sea salt and fresh thyme and enjoy!