Melt the butter in a heavy pan over medium high heat.
When the butter melts and sizzles add the onions, carrots, and the celery.
Saute until the vegetables are tender and begin to caramelize - about 5 minutes.
Remove the vegetables carefully to a plate, leaving as much of the melted butter and juices in the pan as possible.
Set aside.
Pat the chicken dry with paper towel and add it carefully to the hot pan.
Saute until the chicken pieces are golden brown and have reached an interior temperature of 165F.
Remove the chicken from the pan to the vegetable plate and set aside. Keep as much of the butter and juices in the pan as possible.
Add the cauliflower and 1/4 cup chicken stock to the pan and quickly cover.
Reduce heat to medium and cook for about 10 minutes, or until the cauliflower is very tender. Add more stock as necessary to keep liquid in the pan.
Remove from pan and carefully puree in blender until smooth and creamy. Return to the pan.
Add the remaining chicken stock and the heavy cream to the pan along with the herbes de provence.
Bring to a simmer, stirring occasionally.
Stir in the vegetables, chicken, and Hatch chiles.
Bring to a simmer and simmer until the stock is reduced to your preference. Add more stock if it's too thick.
Notes
This can be made in a slow cooker - put everything except the cream in the slow cooker without precooking and cook on low for 6 to 8 hours. Add cream 15 minutes before serving.