Generously coat the inside of a 6-quart slow cooker with cooking spray. (See recipe notes if using a smaller slow cooker.)
Place a layer of potato slices in the bottom of the slow cooker, alternating the Yukon Golds and sweets. Generously sprinkle with kosher salt and black pepper (do not skimp or the potatoes will be bland). Repeat with a second layer of potatoes, another sprinkling of salt and pepper, then another layer of potatoes, continuing until all the potato slices have been used.
Melt the butter in a medium saucepan over medium heat with the onion. Sauté until the onion is soft and beginning to turn translucent, about 4 minutes. Sprinkle the flour over the top, then whisk constantly until it turns a golden color and smells nutty, about 1 minute. Add the garlic and cook 30 seconds. Slowly pour in the milk a few splashes at a time, whisking constantly to smooth any clumps. As you add the milk, the mixture should begin to form a paste that becomes increasing golden. Finish adding the milk, then increase the heat to medium high. Let cook, stirring constantly, until the sauce bubbles and thickens, about 6-8 minutes. Remove the pan from the heat, then stir in the nutmeg, grated cheese, and half of the thyme. Continue whisking until the cheese melts and you have a smooth, rich sauce. Add 1/4 teaspoon kosher salt and 1/8 teaspoon black pepper. Taste and add additional salt and pepper as desired.
Pour the sauce evenly over the potatoes, then jiggle the slow cooker gently so that the sauce seeps down to the various layers. Do not stir. Drape a triple layer of paper towels over the top of the slow cooker so that the sides of the paper towels overhang the edge, then cover the slow cooker with the lid over the top of the paper towels****. Cook for 2 1/2 to 4 hours on high, until the potatoes are tender, changing out the paper towels halfway through if they become soggy. The cooking time can vary widely depending upon your slow cooker, so adjust accordingly. Start checking at the 2 1/2 hour mark, then every 15 to 30 minutes afterward depending on how the potatoes are progressing.
Once the potatoes are tender, uncover and sprinkle with Parmesan cheese and remaining thyme. Cook on high, uncovered, for 10 minutes to allow the cheese to melt and the top to crisp. Serve immediately or keep warm in the slow cooker for up to 1 hour.
*I recommend using a mandoline for fast, guaranteed-even slicing of the potatoes. It's important that the slices be the same relative size to ensure even cooking.
**I always recommend grating your own nutmeg from whole nutmeg instead of buying pre-ground. The flavor is spectacular! I use this zester to do it. Otherwise, regular ground nutmeg can be substituted.
***I recommend using full-fat cheese for the recipe, as it melts the most evenly. Low-fat cheese can also be used, but do not use fat free, as it will not melt completely. Avoid pre-shredded cheeses, as they have a powdered coating that prevents caking and thus may not melt properly and can even make the potatoes greasy.
****DISCLAIMER: Please note that using a towel with a slow cooker could be a fire hazard. Proceed at your own risk. I have done it many times over the years with different recipes and different slow cookers and have never had an issue. That said, different slow cookers can reach different temperatures. If this is your first time using the towel method with your slow cooker, I recommend checking the towel an hour into cooking to be sure that it isn’t too hot.
If using a smaller slow cooker, reduce the recipe accordingly to ensure that the potatoes cook completely (if using a 4-quart, reduce to two-thirds of the total recipe; if using a 3-quart, reduce to half, etc.).
I do NOT recommend cooking this recipe on low heat, as the potatoes tend to turn out soggy and will not cook through properly.