Make the beef and tomato sauce: Heat a large Stainless Clad Saute Pan or Enameled Cast Iron Dutch Oven over medium. Add the onions and a pinch of salt and cook until softened and just beginning to brown, 6–8 minutes. Add garlic and cook until fragrant, 30 seconds. Add the beef and cook, breaking it into small pieces, until browned and cooked through. Season with salt, pepper, nutmeg, and sugar. Stir in the tomato puree, reduce to low, and simmer until thickened but still loose, about 20 minutes. Taste and adjust seasoning.

Make the bechamel sauce: Heat a 3 QT Stainless Clad Saucier over medium, melt the butter. Add the flour and whisk continuously until pale golden, 1–2 minutes. Slowly whisk in the milk, making sure no lumps form. Allow to come to a low boil, then reduce to a simmer, whisking often, until thick enough to coat the back of a spoon, 6–8 minutes. Season with nutmeg, salt, and pepper. Keep warm; it should be pourable.

Assemble the moussaka: Preheat oven to 350F.

Slice the eggplant into 1/2-inch rounds, sprinkle with salt on both sides, and let sit on a cooling rack set over a Sheet Pan for 15 minutes to draw out moisture. Slice the bell peppers into 1/4-inch strips.

Heat an Enameled Cast Iron Skillet over medium-high. Add 1 Tbsp. oil, then the peppers, and sauté until softened and browned in spots. Transfer to a bowl and season with salt.

Add enough oil to the same Skillet to reach a depth of about ½ inch and heat to 350F. Pat the eggplant completely dry, then fry in batches until golden brown, 3–4 minutes per side. Transfer to a cooling rack set over a Sheet Pan and season with salt.

In an Oval Gratin Dish, layer eggplant, peppers, and beef-tomato sauce. Repeat until all vegetables and sauce are used.

Pour the hot bechamel evenly over the top, spreading to the edges but not overfilling. Sprinkle with mozzarella.

Bake until the top is browned and bubbling, 40–50 minutes. Let cool for 10 minutes. Garnish with parsley before serving.