Preheat oven to 400 degrees.
In a large pot heat the butter and oil till very hot. In batches, add the chicken thighs and cook till brown, then flip and cook till brown on the other side, then remove to a plate while cooking the next batches. The chicken will not be cooked in the center.
When done, add the garlic cloves to the pan and cook for just a minute or two before adding the white wine to deglaze the pan. Whisk and scrape the bottom of the pan to remove all the delicious brown pieces. Then add the broth and bring to a boil. Taste the gravy and add salt and pepper to taste
Add the potatoes and bring to a boil, then pour into a 9x13 pan. Top with the chicken thighs and place in the preheated oven. Bake for 50 minutes - 1 hour, flipping the chicken thighs when they get brown on top, roughly 30-40 minutes through baking.
5 minutes before baking is done, stir together the cornstarch and gravy mix with a little water. Pour over the gravy and stir in, then return to the oven to thicken. Once the potatoes are soft, chicken is browned on both sides and gravy is thickened, you're ready to serve!
To make this dish a little quicker you can bake just until the potatoes are cooked then broil to brown(and finish cooking if necessary) the chicken. This works just as well and can save a little time.