Heat oven to 350˚F, and arrange a rack in the middle. Heat a large, ovenproof frying pan over medium-high heat and add bacon. Cook, stirring occasionally, until bacon is crisp and browned, about 6 minutes. Remove bacon with a slotted spoon to a paper towel-lined plate and set aside.
Return pan with bacon drippings to medium-high heat and add onion. Season with salt and freshly ground black pepper and cook until soft, about 2 minutes. Add mushrooms and herbs, and season again with salt and freshly ground black pepper. Cook, stirring occasionally, until tender, about 2 minutes. Add 1/2 cup of the wine and cook until all liquid is absorbed. Remove from heat to cool completely. Meanwhile, prepare chicken breasts.
Cut each breast in half horizontally. Place breasts on a cutting board in a resealable plastic bag or between two pieces of plastic wrap. Using a mallet or the bottom of a pan, pound chicken pieces to an even thickness, about 1/4 inch thick. Season chicken all over with salt and freshly ground black pepper.
Lay chicken breasts on a cutting board so the narrow end faces you. Stir reserved bacon into mushroom mixture and place 1/4 of the mixture halfway up each chicken piece. Fold the bottom piece of chicken up over the filling to enclose it, then roll into a tight cylinder. Use toothpicks to secure the rolls and repeat with remaining chicken and filling.
Heat the large ovenproof frying pan over medium-high heat and add olive oil. Once oil shimmers, place chicken in pan seam-side down and cook, undisturbed, until golden brown, about 4 to 5 minutes. Turn chicken pieces over then transfer pan to oven and cook until filling is warm and interior of chicken is white but still juicy, about 8 to 10 minutes.
Remove chicken to a clean plate and cover with foil. Place pan over medium-high heat, add remaining 1/2 cup wine and broth, and scrape up any brown bits stuck on bottom of pan (be careful, handle will be very hot). Cook over medium-high heat until alcohol is cooked off and sauce is reduced by half, about 4 minutes. Remove pan from heat, stir in butter, and season to taste with salt and pepper. Pour over chicken and serve.
Beverage pairing: Qupé Santa Ynez Valley Marsanne, California. Marsanne is an earthy, round white wine that doesn’t make a big deal of itself, but is a wonderful complement to a great many things. Qupé’s version is classic and direct, with the correct floral, peach, and mineral notes. It’s a subtle wine, but will be a great backup to this simple, fully flavored dish.
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