Place dried porcini mushrooms in a heat-safe bowl and pour the water over them. Steep for 10 minutes or until soft. Let cool. Gently squeeze excess water back into the bowl (once strained, this will be your mushroom stock for step 7). Mince the mushrooms and set aside.
Fold a thin kitchen towel in half over a measuring cup. Slowly pour the liquid through the towel to strain it (you can also use cheesecloth). Set the mushroom stock aside.
In a 12-inch skillet, heat 3 tablespoons oil over medium heat. Add shallots and cook for 2 minutes, until they begin to brown. Add garlic and cook for a few seconds, until fragrant.
Add baby bella mushrooms and cook 2–4 minutes, until they’ve released their liquid and browned. Add porcini mushrooms (from step 1) and cook for 1 minute. Stir in Worcestershire sauce.
Crush the dried tarragon between your fingers and add it to the skillet. Add the fresh tarragon, thyme, garlic powder, and salt. Stir again and remove from the heat.
Stir in chestnuts, panko, and 4–6 tablespoons of the reserved mushroom stock (from step 2). The filling should be moist but not wet.
Divide the contents of the skillet into six equal portions. Working with one chicken breast at a time, spread a potion of filling along the length of the breast and carefully roll it up. Secure with two toothpicks. Repeat with remaining chicken breasts and filling.
Place in a covered dish and refrigerate for 1 hour or overnight.
Preheat oven to 375°F.
In a 12-inch skillet, heat remaining 3 tablespoons oil over medium-high heat. When the oil is shimmering, add the chicken. Cook 1–2 minutes per side, until golden brown.
Cover the skillet with an oven-safe lid and place in the oven. Cook 15 minutes, then transfer the skillet from the oven to the stove. Remove the toothpicks and discard.
Add the Cognac over medium heat. As it begins to simmer, scrape up any brown bits from the pan. Add the chicken or vegetable stock and sprigs of fresh tarragon, and simmer for 2 minutes, until the liquid has reduced by half.
Remove 2 tablespoons of sauce from the skillet and add to a small bowl. Add the cornstarch and whisk together until smooth to create a slurry. Add the slurry to the skillet and simmer for 1 minute, or until the sauce has thickened. Remove from the heat and stir in the butter alternative. Taste and season with salt as needed.
Remove the chicken to a cutting board and slice. Arrange the slices on a serving platter and spoon sauce over them (alternately, you can put a few slices on each plate with the sauce underneath, as pictured). Sprinkle with parsley (if using) and serve.
Notes
I highly encourage using dried porcini mushrooms, as listed, to deepen the flavor of this dish. If you can’t find them, substitute any fresh mushrooms and use extra chicken stock instead of mushroom stock.
If you don’t have cognac, you can use dry white wine.
Don't want to butterfly chicken breasts? Use skin-on chicken breasts and stuff the filling under the skin or skin-on boneless chicken thighs
Make this recipe Passover friendly swap the breadcrumbs for matzah meal and cornstarch for potato starch.