Using a sharp knife or mandolin, finely slice the potatoes to about a 1/16th of an inch or as thinly as you can.
In a large saucepan over medium low heat, melt the remaining 2 tablespoons of cultured butter. Once melted, whisk in flour, stirring to combine. Allow to cook for one minute, then whisk in heavy cream and chicken stock, creating a bechamel. Cook for 3-5 minutes, whisking occasionally, until mixture thickens enough to coat the back of a spoon. Remove from heat, stir in garlic and thyme, and allow to cool slightly.
Place potatoes and half of the gruyere into a large bowl. Pour in bechamel and, using your hands, toss to combine, coating the potatoes evenly with sauce and cheese.
Pick up a handful of the potatoes at a time, arranging them upright in the buttered pan. Repeat with the remaining potatoes until you have 3 columns of potato slices. Pour the leftover bechamel evenly over the potatoes. Sprinkle with the remaining half of gruyere and parmesan. Cover the pan with tinfoil to prevent it from browning too quickly.
Bake for a half hour at 400°F and then remove the tinfoil. Bake for another half hour, or until the bechamel is bubbling and the potatoes are golden brown and cooked through.
Allow to cool for ten minutes before serving with your favorite meal!