In a deep skillet heat 2 turns of the pan extra-virgin olive oil over medium-high heat. Add chicken and lightly brown, 3 minutes, add carrots, onions, and celery as you chop. Season with salt and pepper and cook 10 to 12 minutes to soften.
Preheat broiler. Set rack in middle of oven.
Bring 1 cup chicken stock and 1/2 cup cream to a boil, stir in polenta and whisk, 3 minutes. Turn heat low, stir in Gruyere cheese and reserve.
*You may need up to 3/4 to 1 cup of polenta to fill the tops of your soup bowls or use some more of the remaining stock. Scoot meat and veggies off to side, melt butter and combine with flour 1 minute. Whisk in 2 cups stock and combine, stir in 1/2 cup cream and bring to a bubble. Stir in Dijon, tarragon, peas and adjust salt and pepper and transfer to soup bowls. Set soup bowls on baking dish. Form tops to your pot pies with the polenta and cheese mixture. Set under broiler and brown 2 to 3 minutes.