Preheat oven to 400.
Cut the corn off the ears, set aside.
In a large pot, melt 2 tbs butter. Add the shallots and cook until softened, about 3 minutes. Add the carrots, peas, and celery, cook until the vegetables have soften about an additional 5 minutes. Remove from pot, set aside.
Heat the olive oil. Add the chicken, cook until browned on all sides, about 5 minutes, remove chicken from pot.
Add remaining 2 tbs butter, heat until melted. Spinkle flour on top, whisk until well combined. Add the chicken broth and bring to a low simmer. Return the chicken and vegetables to the pot along with the corn, allow to simmer for about 10 minutes.
Place 6 individual, oven safe bowls (about 1 ½ cup sized) on a baking sheet. Pour chicken soup into bowls until about 2/3 full.
Ina large bowl, add the cornmeal, flour, baking powder, salt and stir until combined. Make a well in the dry ingredients, add the beer, egg and melted butter. Stir until just combined.
Top the bowls with cornbread mixture (it’s OK if the batter sinks, it’ll rise during baking).
Bake at 400 for 20 minutes or until cornbread is golden brown.