Preheat oven to 400 degrees.
Melt 1/2 T butter in a non-stick pan over medium-low heat. Add the chicken and cook until cooked through, about 8 minutes. Set the cooked chicken aside. Melt the remaining butter and add in the onion, celery and carrots and cook stirring occasionally until the veggies start to soften.
Reduce heat and add in the flour. Make sure to coat all the veggies with the flour. Stir in the broth and bring to a boil. Reduce the heat to medium and simmer for 5 minutes, stirring constantly. Add in peas, cream cheese, thyme, salt and pepper.
Stir until the mixture is thickened and the veggies are tender, about 8 minutes. Add the chicken back in and stir until heated through.
Divide the mixture into the 8 ramekins. Put one uncooked crescent roll on each of the ramekins. Bake for about 10 minutes. Remove from the oven and let cool about 5 minutes.