Preheat oven to 400.
Place your minced garlic in the butter and mix together with a fork.
Coat the bottom of a 10" skillet with some of the melted butter mixture. Place 1 potato slice in the center and then make a spiral pattern, overlapping potatoes until bottom of pan is covered. Season with a little salt and pepper. Repeat entire process with remaining potatoes, being sure add butter to the top layer of potatoes.
Place skillet over medium/high heat for about 5 minutes, until butter is sizzling.
Transfer skillet to oven and cook until potatoes are nicely browned and beginning to pull away from the edge of the pan, about 20 minutes.
Remove from oven and invert galette onto a plate or platter.
Grate fresh parmesan cheese on top just before serving.