Chicken Pot Pie Buns

Name: Chicken Pot Pie Buns
Ingredients: 2 tbsp. butter; 1/2 c. carrot, 1/4 cubed; 1/4 c. celery, finely chopped; 1/2 small onion, finely chopped; 1 clove garlic, minced; 1 tsp. fresh thyme leaves, roughly chopped; Kosher salt; Fresh ground black pepper; 2 tbsp. all-purpose flour; 3/4 c. low-sodium (or homemade) chicken stock; 3 tbsp. heavy cream; 1/2 tbsp. soy sauce; 1/8 tsp. ground nutmeg; 1/4 c. frozen peas; 3/4 c. cooked chicken breast, 1/4 cubed; 1/3 c. bread flour; 3/4 c. water; 2 1/2 c. bread flour; 1/3 c. granulated sugar; 3/4 tsp. kosher salt; 1 package instant yeast; 3 tbsp. evaporated milk; 2 large eggs + 1 egg yolk, separated; 2 tbsp. softened butter; Cooking spray; 1 tsp. whole milk; White and black sesame seeds, optional