Slice the eggplants, zucchini, and potatoes into ¼-inch rounds. Sprinkle salt over the eggplant slices and let them sit for 30 minutes to draw out excess moisture. Rinse and pat dry before cooking.

Heat olive oil in a skillet over medium heat. Fry the salted eggplant, zucchini, and potato slices in batches for about 3-4 minutes per side. Drain on paper towels.

In a large pot, sauté the chopped red onion over medium heat until translucent, about 5 minutes. Add minced garlic, stirring for another minute. Incorporate ground meat, browning it for approximately 6-8 minutes, then deglaze with red wine and simmer briefly.

Pour in crushed tomatoes along with cinnamon, nutmeg, oregano, and thyme. Let the sauce simmer for 10-15 minutes on low heat until it thickens. Stir in chopped parsley just before removing from heat.

In a saucepan, melt butter over medium heat. Whisk in gluten-free flour and cook for about 2 minutes. Gradually add milk while whisking until thickened, around 5-7 minutes. Blend in egg yolks and nutmeg.

Preheat your oven to 350°F (175°C). Layer potato slices at the bottom of a greased baking dish, followed by eggplant and zucchini. Season each layer with salt, pepper, and cheese. Finish with the meat sauce on top.

Spread the béchamel sauce over the layered moussaka and sprinkle more cheese on top.

Bake for 40-45 minutes until golden brown. Cover with foil at the 30-minute mark to prevent over-browning.

Let the moussaka rest for at least 30 minutes before slicing for easier serving.