Preheat the oven to 350 degrees F and position one of the racks in the center.
Heat the olive oil in a large saucepan. Add the garlic and bay leaf and cook for about 30 seconds, then add the crushed tomatoes, tomato sauce, tomato paste and wine. Season with parsley, sugar, Italian seasoning, ground fennel, salt and pepper. Simmer, covered, stirring occasionally, 15 to 20 minutes.
Heat a cast-iron grill pan over medium-high heat. Add the squash and zucchini to a large bowl, and toss with the extra-virgin olive oil, salt and pepper. Add the vegetables to the grill pan in a single layer, working in batches if necessary. Grill until softened and there are grill marks, about 4 minutes per side.
Mix the ricotta with the milk, Parmesan, egg, 1 cup mozzarella and a few pinches salt and pepper in a large bowl. Set aside.
Spread a thin layer of the pasta sauce (about a third) on the bottom of a 9-by-13-inch baking dish. Add a layer of noodles (about 5), breaking to cover the entire dish in a single layer. Layer on half of the grilled veg, then half of the ricotta mixture and another third of sauce. Repeat the layers, finishing with the veg on top. Sprinkle the remaining mozzarella on top in an even layer. Place the whole basil leaves on top.
Cover the baking dish with aluminum foil and bake for 30 minutes. Remove the foil and continue baking until lightly browned on top, another 15 to 20 minutes. Let rest for about 10 minutes before slicing.