Finely chop the onions, garlic, chili peppers, butternut squash, mushrooms, and tomatoes. Preheat oven to 180°C (350°F).

Heat 2 tbsp oil in a large pan over medium heat. Add onions and garlic; cook for 3–4 minutes until soft.

Add chili peppers, butternut squash, and mushrooms. Cook, stirring, until vegetables are translucent and starting to soften (6–8 minutes). Season with salt, black pepper, and oregano.

Add chopped tomatoes, 1 cup tomato puree, and 2 cups vegetable stock to the pan. Bring to a simmer and reduce heat. Let simmer for 12–15 minutes until the sauce thickens and concentrates. Taste and adjust seasoning.

In a separate saucepan, melt 1 tbsp butter over medium heat. Stir in 1 tbsp flour and cook for 1 minute to form a roux.

Gradually whisk in 3 cups milk a little at a time to avoid lumps. Cook, whisking, until the sauce coats the back of a spoon and thickens (5–7 minutes). Remove from heat and stir in grated cheddar (reserve some for the top). Season with salt and a little black pepper.

While sauces finish, bring a large pot of salted water to a boil. Add lasagna sheets and cook for 6–8 minutes (follow package for exact timing) until pliable but not falling apart. Drain and lay sheets flat on a lightly oiled tray.

Lightly oil or spray a large ovenproof dish. Spread a thin layer of ragu across the bottom. Pour a layer of béchamel over the ragu.

Lay lasagna sheets over sauces. Repeat layers (ragu → béchamel → pasta) until ingredients are used, finishing with béchamel and a generous sprinkle of reserved cheddar on top.

Place the dish in the preheated oven and bake for 20 minutes at 180°C (350°F). For a golden top, switch to grill/broil for 2–3 minutes—watch carefully.

Remove from oven and let rest for 10–15 minutes for cleaner slices.