Preheat the oven to 180 degrees.
Toss the cauliflower in a bowl with 1 tablespoon of the olive oil and 1/2 teaspoon salt. Spread the florets in an even layer on a baking sheet and roast, tossing once, until tender and golden brown in spots, 30 to 35 minutes. Cool slightly.
Put the tomatoes in a medium bowl and use your hands to crush them. Rinse the can with 1 1/2 cups water and add it to the bowl of tomatoes.
Heat the remaining tablespoon of oil with 4 cloves sliced garlic and 1/2 teaspoon salt in a small Dutch oven over medium heat until the garlic begins to sizzle and becomes aromatic, about 2 minutes. Add the bell pepper and cook, stirring, until soft, about 8 minutes. Add the tomato paste and stir to incorporate, about 30 seconds. Add the crushed tomatoes with their juice and 4 large leaves of basil. Bring to a boil, reduce the heat and simmer, stirring occasionally, until the sauce is thickened, about 40 minutes. You should have about 3 3/4 cups of sauce.
Meanwhile, bring a large pot of water to a boil. Drop the lasagna noodles one at a time into the pot. Cook according to the package directions until al dente. Drain the noodles in a colander. Add 1 to 2 teaspoons oil to the noodles, tossing to coat to prevent them from sticking, and drape over the side of a large bowl.
Combine the ricotta, egg, 1 1/2 cups of the roasted cauliflower and 1 chopped clove garlic in a food processor and pulse until evenly pureed. Tear the remaining basil into small pieces, add to the food processor and pulse 3 to 4 more times to chop the basil finely, but not puree. Transfer the mixture to a medium bowl.
Assemble the lasagna: Spread a thin layer of sauce (around 1/4 cup) on the bottom of a 9-by-13-inch baking dish. Lay 4 of the noodles on the bottom, without overlapping, cutting to fit, if necessary. Spread with half of the cauliflower-ricotta mixture, followed by half of the roasted cauliflower, one-third of the tomato sauce, one-third of the mozzarella and one-third of the Parmesan. Loosely fit 3 more noodles on top of the cheese without overlapping. Spread with the remaining cauliflower-ricotta mixture, followed by the remaining roasted cauliflower, one-third more of the tomato sauce, one-third more of the mozzarella and one-third more of the Parmesan. Top with the remaining 4 lasagna noodles, cutting just to fit. Then add the remaining tomato sauce, mozzarella and Parmesan. Cover with foil and bake until bubbly and hot, about 20 minutes. Remove the foil and cook until the cheese begins to brown, about 10 minutes more. Allow to rest for 10 minutes so the lasagna will cut more easily. Garnish with the parsley.