Preheat your grill to medium-high.

Slice the eggplant, zucchini, and yellow squash into ½-inch thick slices. Brush both sides lightly with olive oil and season with salt and pepper.

Grill the vegetables in batches, 4–5 minutes per side, until tender and marked with char lines. Transfer to a tray to cool.

Grill the red bell peppers whole, without oil, turning occasionally until the skins are blackened and blistered on all sides.

Place the hot peppers in a bowl and cover, or pop them into a plastic bag, and let them steam for about 30 minutes to loosen the skins.

Peel off the charred skins, remove stems and seeds, then roughly chop the peppers.

Once all the vegetables are cool enough to handle, chop the grilled eggplant, zucchini, and squash into ¼–½ inch pieces and set aside.

If using dried or fresh ready-made lasagna sheets, cook according to package directions until just al dente. Drain and lay flat on a lightly oiled sheet pan to prevent sticking.

If using homemade pasta, prepare the dough and let it rest in a lightly oiled bowl covered with a damp cloth. Roll out each sheet just before layering so it doesn’t dry out.

Heat 1 tablespoon olive oil in a large pan over medium heat.

Add the chopped onion and cook 4–5 minutes, until softened and translucent.

Stir in the garlic and red pepper flakes and cook about 30 seconds, until fragrant.

Purée half of the canned diced tomatoes (with their juices), then add both the puréed and remaining diced tomatoes to the pan along with ½ cup water.

Simmer for about 3 minutes to let the flavors come together.

Stir in all the chopped grilled vegetables and the fresh spinach. Cook just until the spinach wilts and everything is well combined.

Season with salt and pepper to taste, then remove from the heat and set aside.

In a large bowl, combine the ricotta, pecorino romano, eggs, chopped fresh basil, ½ teaspoon salt, and a few grinds of black pepper.

Stir until smooth and evenly combined. Set aside.

Preheat the oven to 350°F (175°C). Lightly oil a 9 x 13 x 2-inch baking dish.

Spoon about 1 cup of the veggie filling into the bottom of the dish and spread into an even layer.

Add a layer of pasta sheets to cover the sauce.

Spread half of the cheese mixture over the pasta. Sprinkle with one-third of the shredded mozzarella. Top with one-third of the veggie filling.

Add another layer of pasta. Spread the remaining cheese mixture over the pasta, then add another third of the mozzarella and another third of the veggie filling.

Finish with a final layer of pasta and the remaining veggie filling. Top with the last of the mozzarella and crumble the goat cheese evenly over the surface.

Cover the dish loosely with lightly oiled foil and bake for 30 minutes.

Remove the foil and bake for another 15 minutes, or until the lasagna is bubbling around the edges and the cheese is nicely browned on top.

If you like an extra-golden top, switch the oven to broil for 1–2 minutes, watching closely so it doesn’t burn.

Let the lasagna rest for at least 20–30 minutes before cutting and serving so the layers can set and the juices reabsorb.