Slice the potatoes to 1/8″ thick. (Julia suggested to peel them but I didn’t). Put the sliced potatoes in a large bowl of cold water and let them sit, drain when they’re ready for use and dry with a paper towel.
Preheat the oven to 425 degrees
Grease a 3.5-quart dish or a 9X9 glass pan with butter, about a ½ tablespoon. Make sure to rub the sides and bottom. Add the minced garlic to the dish, making sure to spread it all over the bottom and sides too.
Using half of the potatoes, layer them to cover the bottom overlapping one another. It will look like at least two layers of potatoes.
Season the potatoes with 1/2 teaspoon salt and 1/8 teaspoon of pepper. Sprinkle the potatoes with 1/2 cup of cheese and 1 tablespoon of butter (dice the butter into small pieces). Top with half of the cheese.
Arrange the remaining potato slices over the first layer, and sprinkle with remaining salt, pepper, cheese, and butter (diced).
Warm up the milk and chicken broth in a microwavable bowl or in a sauce pan over the stove until its boiling. Pour the mixture over the potatoes. (the original recipe calls for just milk, but the broth/stock adds more flavor)
Set baking dish over the stove until simmering, set in the oven. Bake for 25-30 minutes or until potatoes are tender, milk has been absorbed, and the top is browned.