Preheat the oven to 400°F. Set four 12-ounce ramekins on a baking sheet, or use an 8-cup baking dish about 2-inches deep.
In a 1-quart saucepan, bring the stock or broth to a simmer. Add the carrots and cook until crisp-tender, about 10 minute. using a slotted spoon transfer the carrots to a plate and turn off heat under the stock or broth.
1 1/2 cups chicken stock, 1 medium carrot
Meanwhile, in a 10-inch sauté pan or skillet, melt the butter with the oil over medium heat until the butter foams. Add the onion and sauté until it begins to soften, about 2 minutes.
Add the mushrooms and sauté until they just begin to brown, about 3 minutes more. Sprinkle the flour over the onion-mushroom mixture and stir to dissolve. Immediately add the stock or broth, bring to a simmer, and stir until smooth and thickened, about 2 minutes.
8 oz mushrooms, 2 tbsp flour
Add the cream, stir to blend, and bring to a simmer. Add the chicken, carrots, and parsley, bring to a simmer, then add salt and pepper. Remove form heat.
1/2 cup heavy cream, 1/2 large chicken, 1/2 cup parsley
Divide the chicken mixture among the ramekins or spoon it into the baking dish. Place 2 frozen biscuits on top of the chicken mixture in each ramekin, or evenly space them on top of the chicken mixture in the baking dish. bake for 12 minutes, or until heated through. Serve immediately.