For the biscuits: Preheat the oven to 425 degrees F. Whisk the self-rising flour and baking soda together. Then cut the cold butter into the dry ingredients. Mix until it resembles sand. In a separate bowl, whisk together the buttermilk, thyme and 1 teaspoon crushed pepper. Add the buttermilk mixture to the flour and butter mixture and, using a rubber spatula, mix until just combined. Do not over mix!
On a silicon-lined baking sheet, scoop about a 1/4 cup of the batter to form each biscuit, leaving about 2 inches between each biscuit. Brush each with melted butter and sprinkle with crushed pepper. Bake until golden brown, about 15 minutes. Let cool on wire rack.
For the filling: In the same oven, bake the chicken on a parchment-lined baking sheet until the internal temperature on an instant-read thermometer reaches 160 degrees F, 20 to 25 minutes. Let cool, remove the skin and shred.
Heat a large saute pan over medium heat. Melt the butter, add the carrots and onions and season with salt and pepper. Saute until the veggies are soft, 6 to 8 minutes. Add in the all-purpose flour and cook until blonde, about 2 minutes. Add the dry sherry, and then whisk in the heavy cream, chicken stock and thyme sprig. Simmer until thickened, about 10 minutes. Remove the thyme sprig and adjust the seasoning.
For the sweet pea pesto: Put the peas, parsley, pine nuts and lemon juice into a food processor. Pulse until combined, and then slowly drizzle in the olive oil. Season and set aside.
For the sandwich build: Split the warm biscuits with a fork. Place some shredded chicken on the bottom buns, top with some pot pie filling and schmear the sweet pea pesto on top. Close and eat.