For the filling: Place the chicken breasts in a large stockpot along with 2 teaspoons of the salt and enough water to cover. Bring to a boil, reduce the heat and simmer until the chicken is tender, about 30 minutes. Remove the chicken to a plate to cool, reserving 3 cups of the broth; supplement with canned chicken stock if you are short. When cool enough to handle, cut the chicken into bite-size pieces.
While the chicken is cooking, combine the potatoes and the remaining 2 teaspoons salt in a medium stockpot. Fill with water to cover and bring to a boil over high heat. Lower the heat and cook until the potatoes are tender but not mushy, 15 to 20 minutes. Drain the potatoes in a colander and set aside to cool.
Melt 4 tablespoons of the butter in a large saucepan over medium heat. Add the carrots and cook for 5 minutes. Add the celery, onion and a pinch of salt and pepper; cook until the onions are soft and almost translucent, 4 to 5 minutes. Add the remaining 4 tablespoons butter and, once melted, add the flour to make a roux. Cook the flour for 2 minutes, stirring constantly, then add the milk and reserved chicken broth. Simmer, stirring frequently, until the mixture thickens, 5 to 7 minutes. Stir in the chicken, corn, peas, celery seeds and garlic powder. Remove from the heat.
Grease eight 10-ounce ramekins with butter and place on a large, rimmed baking sheet or jellyroll pan. (Alternatively, grease one 9-by-13-inch baking dish.)
Evenly divide the potatoes among the ramekins. Spoon the filling over the potatoes, leaving about 1/4-inch of space at the top for the crust.
For the crust: In a large mixing bowl, whisk together the baking mix and pepper until well blended. Whisk in the melted butter and buttermilk until smooth. Stir in the Parmesan. Pour some batter into each ramekin and smooth over the top, being careful not to mix it into the filling. Bake until the crust is crispy and nicely browned, 40 to 45 minutes. Let sit for 10 minutes before serving.