For the tomato sauce: Heat the oil in a medium saucepan over medium-high heat. Add the onions and cook until soft. Add the garlic and red pepper flakes and cook for 30 seconds. Add the tomatoes, breaking them up with a wooden spoon, and the basil and cook until thickened and the tomatoes soften and break down. season with salt and pepper.
Transfer to a blender and blend until smooth. Return the mixture to the saucepan, add the basil and chopped parsley, season with salt, pepper, and honey, if needed.
For the cauliflower sauce: Preheat the oven to 350 degrees F. Remove the florets from the head of cauliflower and put in a small roasting pan. Drizzle with olive oil and season with salt and pepper. Add 1 1/2 cups water to the bottom of the pan, cover with foil, and cook until very tender, about 1 hour. Remove and increase the oven temperature to 375 degrees F.
Melt the butter in a medium saucepan over medium heat. Whisk in the flour and cook for 30 seconds. Slowly whisk in 4 cups of the milk, increase the heat and bring to a boil, whisking constantly. Cook until thickened, about 5 minutes. Add the cauliflower, reduce the heat to low, and cook for 5 minutes longer. Remove from the heat and let cool slightly. Transfer the mixture to a blender (in batches) and puree until smooth. Strain the mixture into a clean saucepan through a medium mesh strainer and bring to a simmer over low heat. Whisk in the nutmeg, cheese, and salt and pepper, to taste. Cook for 1 minute. Add some of the remaining warm milk, if needed.
For the lasagna: Increase the oven to 375 degrees F. Combine the ricotta, egg, 1/2 cup parsley, 1 teaspoon thyme, and romano cheese in a bowl and season with salt and pepper. Cover and refrigerate until ready to use.
Heat the olive oil in a large saute pan over high heat. Add the garlic cloves and cook for 1 minute. Add the mushrooms and cook until they begin to soften. Add the shallots and cook until golden brown and completely dry. Drain the porcini mushrooms, reserving the soaking liquid, coarsely chop, and add to the mushrooms in the pan and cook for 1 minute. Deglaze with the porcini soaking liquid and cook until completely reduced. Stir in the remaining 2 teaspoons thyme, remaining 1/4 cup parsley, and season with salt and pepper. Remove from the heat.
To assemble: Ladle some of the tomato sauce into the bottom of a 10 by 14 by 2 1/2-inch baking dish. Ladle some of the cauliflower mornay sauce over the tomato sauce. Top with 4 noodles. Top the noodles with some of the ricotta mixture, then some mushrooms, fontina, and romano. Season with salt and pepper. Repeat to make 4 layers. Ladle the cauliflower mornay sauce over the top of the noodles, making sure to cover the noodles completely with the sauce, and sprinkle with more of the romano cheese. Put the lasagna pan on a baking sheet, cover with foil, and bake for 30 minutes. Remove the foil and continue baking until bubbly and the top is golden brown, 30 to 40 minutes longer. Remove from the oven, sprinkle the top with parsley, and let rest 15 minutes before serving. Cut into squares and serve additional tomato sauce on the side.