Preheat the oven to 425 degrees.
Melt the butter in a 3 qt. (or larger) pot or saucier. Once melted, add it carrots, peas, and corn (or vegetables of choice).
Cook the vegetables in the butter until they begin to soften, stirring occasionally. This will take about 5-7 minutes.
Add in the flour and mix until until combined. Let cook about 1 minute longer.
Slowly pour in the chicken broth and whisk until no lumps of flour remain.
Add in the heavy cream and milk. Whisk to combine and let boil until the mixture becomes slightly thicker. Continue to whisk occasionally, to prevent burning on the bottom of the pot.
Once the mixture is thick and bubbling, stir in the chopped chicken. Pour the entire mixture into the bottom of a 9x9 pan, or a cast iron skillet.
Bake for 20-25 minutes, or until the biscuits are golden and cooked through.