Preheat oven to 425°F. In a 6-quart stockpot, melt the butter and sauté the onion and celery with 1 tsp salt over medium-low heat. Sauté until the onion is soft and translucent but not browned, 6-8 minutes.
While the onion and celery are sautéing, prepare the roasted vegetables. Place the carrots, sweet potatoes, and chicken breast on a large sheet pan. Drizzle with olive oil, salt, and pepper. Roast in preheated oven until the chicken registers 160°F and the vegetables are tender when inserted with a knife. Remove from oven and set aside.
Once the onion and celery are soft and translucent, add the flour. Stir and cook the flour until it is slightly toasted and just starting to stick to the bottom of the stockpot, 3-4 minutes. Pour in the white wine, Dijon mustard, and thyme. Whisk until smooth. At first, the flour will be clumpy. Continue to whisk and add the chicken stock until the mixture is smooth and thick. Stir in the pearl onions and peas to warm through, 2 minutes. Remove from the heat and add the roasted carrots, sweet potatoes, and shredded chicken. Pour into a greased 9x9-inch baking dish and prepare biscuits.
In a large bowl, combine the flour, baking soda, baking powder, salt, and sugar. Stir to combine. Add the diced butter and, using a pastry cutter or hands, work into flour until it resembles a coarse grainy texture. Add buttermilk and stir. The dough will be shaggy and almost batter-like.
Scoop biscuits onto the top of the prepared filling, making approximately nine biscuits. Sprinkle with salt and bake in the preheated oven until the biscuits are golden and the filling is bubbling, 30-40 minutes. Remove from oven and cool 10 minutes before serving.