Preheat the oven to 400°F.

To make the filling for the pot pie: If using fresh pearl onions, fill a small saucepan with water and bring to a boil over medium-high heat. Add the pearl onions and blanch for about 3 minutes. Drain and set aside to cool. Peel the onions using a small paring knife, and set aside.

In a large saucepan, melt the butter over medium heat. Add the carrots, celery, and onion and slowly cook the vegetables for about 10 minutes, stirring occasionally, without letting them color. Add the flour to the pan and cook, stirring frequently, for 5 to 6 minutes. Add the chicken stock, slowly at first, stirring vigorously to incorporate it with the vegetables.

Add the potatoes and chicken, bring to a simmer, and cook for about 10 minutes, or until the potatoes are tender. Add the peas and pearl onions and cook for another minute or so to heat through. Season with the salt and with pepper to taste. Transfer to a 13 x 9 x 2-inch baking dish.

To make the topping: Put the butter, cornmeal, flour, sugar, baking powder, salt, and eggs in the bowl of a food processor fitted with a metal blade. Pulse until just combined but still crumbly.

Add the milk and pulse just until incorporated. Pour the batter over the chicken filling to cover completely. Bake for about 40 minutes, or until the crust turns golden and the filling is bubbling around the edges.