Carefully lift the chicken, shallots, and bacon from the pan and transfer them to a warmed serving dish. Discard the spent thyme, rosemary, and bay leaves.
To make the thickener, combine the 2 tablespoons of plain flour, the remaining olive oil, and the 1 teaspoon of butter in a small bowl, mashing them together with the back of a teaspoon until smooth. Bring the wine mixture in the pan to a gentle boil, then gradually drop in small pieces of the thickener, whisking each piece in using a wire whisk until it's fully incorporated and the sauce begins to thicken. Simmer for 1–2 minutes.
Scatter the sautéed mushrooms over the chicken, then pour the rich wine sauce over everything. Finish with a garnish of fresh chopped parsley.