Step 1

Season both sides of the chicken with salt and pepper. Heat the olive oil in a 12-inch nonstick skillet over medium heat until rippling and hot. Add the chicken and cook for about 4 minutes on each side, until golden and cooked through. Don't overcook or you'll have dry chicken (if you have a thermometer, cook until 165 degrees F). Remove to a plate and cover to keep warm.

Step 2

Add the butter to the pan and melt over medium heat. Stir in the shallot, mushrooms, salt, thyme and garlic. Cook, stirring often, until the mushrooms are tender and golden and the liquid has released and most of it has evaporated, 8-10 minutes.

Step 3

Sprinkle the flour over the mushroom/onion mixture and stir while the mixture cooks for 1-2 minutes. Slowly whisk in the broth, adding just a bit at a time and whisking until thick then adding a bit more (this will help the flour to absorb into the liquid and not clump on the mushrooms). Once all the broth has been added and the sauce is smooth, stir in the milk, and simmer the mixture for 5-7 minutes until it is thick and bubbly. Add salt and pepper to taste. Serve immediately over the reserved chicken (this is divine with mashed potatoes).