Preheat oven to 425 degrees.
In a mini food processor, pulse the sage, rosemary and thyme until finely chopped. Add the lemon zest and pulse to combine. Add the salt and pulse until finely ground. Set herb salt aside.
In a large bowl, toss the potatoes with the oil and butter and season with pepper. Spread the potatoes in a single layer on 2 large rimmed baking sheets and roast for 25 minutes. Season the potatoes generously with the herb salt making sure all get coating and continue baking for 5 minutes, or until the potatoes are tender and golden. Transfer to a bowl and keep warm.
While the potatoes are roasting, in a large skillet, heat vegetable oil until very hot. Use paper towels to dry the chicken and season with salt and pepper. Place the breasts skin side down in the hot pan. Leave the breasts alone to brown well. Reduce heat to medium-low and cook for approximately 15 minutes without flipping or moving the chicken. Flip the pieces and cook for an additional 15 minutes, until cooked through.
Remove the chicken from the pan and set aside. In the same pan, discard any excess fat. Then add shallots and thyme and cook for 1 minute. Increase heat to high and pour in white wine. Reduce wine until it's almost completely reduced, approximately 5 minutes. A thick syrup will remain in the pan. Add in the chicken stock and reduce by half. Then stir in lemon juice, lemon zest, and salt and pepper to taste. Add the butter and stir until combined. Place chicken breasts back in the sauce to warm briefly. Serve sliced with potatoes and a hearty spoonful of sauce.