In a deep skillet, heat two turns of the pan of EVOO over medium-high heat. Add chicken and lightly brown, 3 minutes, then add carrots, onion and celery as you chop, then the peas, and season with salt and pepper. Cook for 10-12 minutes to soften.
Pre-heat the broiler. Set rack in middle of oven.
Bring 1 cup chicken stock and 1/2 cup cream to a boil, then stir in polenta and whisk to mass it, 3 minutes. Turn heat low, stir in Gruyère cheese and reserve.
Scoot meat and veggies off to the side in the skillet, then melt the butter and combine with flour for 1 minute. Whisk in the 2 cups remaining stock and combine, then stir in 1/2 cup remaining cream and bring to a bubble. Stir in Dijon mustard and tarragon, adjust salt and pepper, to taste, and transfer to soup bowls.
Set soup bowls on a baking dish. Form tops to your pot pies with the polenta and cheese mixture. Set under broiler and brown for 2-3 minutes.