Place the flour in a shallow bowl. Add the salt and pepper; stir to combine. Dredge the chicken through the flour mixture until coated on all sides. Shake off any excess flour. Set the chicken aside.
Heat the oil in a large skillet over medium-high heat. Add the chicken to the skillet and cook, turning once, until the chicken is golden and just barely cooked through, about 5 to 6 minutes total. Transfer the chicken to a plate and set aside.
Lower the heat to medium. Place the mushrooms in the skillet, stirring and cooking until tender, about 5 to 7 minutes.
Take the skillet off of the heat; add the wine and the chicken broth. Place the skillet back on medium heat, and stir to scrape up any browned bits from the bottom of the pan (this gives the sauce great flavor). Add the garlic and butter to the skillet. This is a good time to add a splash of heavy cream if you like, too. Simmer the sauce until it reduces and thickens slightly, about 5 to 8 minutes. Season with salt and pepper, to taste.
Return the chicken to the skillet, spoon the sauce over top, and continue simmering for a few more minutes so that the chicken warms through.
Serve immediately and garnish with fresh herbs.