Preheat oven to 425 degrees F. Melt the butter in a large skillet or oven-safe pan. Add the onions, carrots, celery, salt, pepper, and thyme; sauté for 5 minutes. The onions will look tanslucent.
Add the flour; stir and sauté for 1-2 minutes. Add the wine and let it soak into the vegetables for a few minutes. Slowly and gradually, add the milk and the chicken broth, stirring after each addition.
The mixture should resemble a thick, delicious creamy soup. Add chicken and peas. Let mixture simmer for 5 minutes, stirring occasionally. See below how to make biscuits: Arrange biscuits on top of filling and brush the top of the biscuits with melted butter for extra browning.
Bake for 15-20 minutes, until hot, bubbly, and biscuits are cooked through and slighly browned.