Wash and remove the ends of the zucchinis. Slice the zucchinis lengthwise to between 1/8 to 1/4 inch thick. Use a mandolin if you have one, it will help you slice the zucchini faster and in perfect consistent slices. Otherwise, slicing with a knife is fine too. Sprinkle the 2 tsp of salt on the zucchini as you go and allow the zucchini slices to sit in a colander or for about 30 minutes. After 30 minutes, run two fingers on either side of the slices, squeezing all the way down over a bowl or the sink, releasing even more water. Place the slices on a clean towel and pat the zucchini very dry. Rub 1 Tbsp of olive oil onto an extra-large baking sheet (or 2 smaller ones) and place the zucchini slices in a single layer. Roast in a 375F oven for about 10 minutes. Allow to cool.
If using fresh tomatoes, deseed the tomatoes (if you wish remove the skins). Bring the tomatoes to a boil and add the minced garlic, chopped basil, crushed fennel seeds, ground oregano, olive oil, sugar, and salt to taste. Simmer until thick and reduced (may take up to an hour). It's important to use a thick lasagna sauce in this recipe because the lasagna can otherwise be on the soupy side without the pasta to soak up the extra liquid as it bakes.
In a large skillet or wok, heat 2 Tbsp olive oil and sauté the onions for 3 to 4 minutes. Add the mushrooms and continue cooking. Once the mushrooms are soft, add the chopped swiss chard. When the chard is cooked, remove from heat and drain any juices (save these for great soup stock). Add 2 Tbsp flour to the mixture and mix well to incorporate.
Oil a 9 x 13 inch lasagna dish and spread about one third of your sauce on the bottom. Add a layer of roasted zucchini to cover the tomato sauce. Add the ricotta and parmesan cheese mixture and spread evenly. Add another layer of zucchini slices. Add a second round of tomato sauce and spread evenly, followed by the vegetable mixture and half of the shredded mozzarella cheese. Add a last layer of zucchini slices followed by the third and last round of tomato sauce. Place the twelve basil leaves on top of the sauce and sprinkle the rest of the shredded mozzarella on top. Place a baking tray on the rack beneath the lasagna pan to catch any bubbling juices from falling to the bottom of your oven. Bake for about 40 minutes at 350F until the cheese is melted. If you wish, turn on the broiler on high for the last 2 minutes to brown the cheese slightly. Allow to sit and cool for 30 minutes before slicing.