Turn oven to 400. If you haven't done it yet, scrub and peel the sweet potatoes and squash. Slice into 1/4"-1/2" thick slices. Bring a shallow pot of salted water to a boil, and par-cook the potatoes and squash for about 15 min to soften a bit (they will continue to cook in the oven, so don't overcook here or they'll fall apart.) You can use a different winter squash, just cut it similarly to your sweet potatoes.
Wash and tear your greens into bite-sized pieces. Finely chop the onion. Heat up 1 tbsp of the butter. Begin to cook the onion in the butter, about 3-5 min. Add in your salt as it softens. Add in the kale in batches, covering with a lid in between additions and stirring occasionally, until it's all totally wilted (about 5-7 more min, depending on how tough it is.)
Warm, but do not boil, the milk or cream with the minced garlic (in the microwave or in a small pot on the stove or in the oven.) Melt the remaining 2 tbsp of butter over medium heat in small pot and then sprinkle in flour, then quickly whisk to make a paste. Cook for 1-2 minutes to burn off the floury taste. Start to stir in the milk and/or cream and minced garlic, the nutmeg and thyme, and turn the heat to low. Continue whisking to thicken. Turn off heat. Stir in the grated cheese and about 1/2 tsp pepper.
Butter/grease the bottom of a casserole dish (9" square or comparable.) On the bottom layer, place half the sweet potato and butternut squash slices. Next, about half of the sautéed kale. Then half of the parsley, and then half of your cheesy béchamel sauce. Repeat all layers one more time, ending with cheese sauce on top. Optional to crack on a little more pepper and maybe a sprinkle of hard salty cheese (grated parm or Flat Rock).
Bake at 400 for 45-55 minutes, until the cheese is bubbling and there is some nice looking browning on top. If it browns too quickly (in our kitchen it did) start with tinfoil on top and remove for the last 20 minutes of cooking.