Cut your zucchini in half horizontally, then cut into skinny strips (the same width as your lasagna noodles) vertically. Spread the “zucchini lasagna noodles” out on several clean dish towels or paper towels and sprinkle generously on both sides with salt. Let the zucchini sit until it’s time to use the noodles, then pat totally dry.
Preheat oven to 375°F.
Warm 1 tablespoon oil in a 12 inch ovenproof skillet over medium-high heat. Add 1 small diced onion and sauté for 3 to 4 minutes, until slightly translucent. Add 1 pound ground chicken and 4 minced garlic cloves and cook, using a spoon to break the meat up until small pieces, until it is no longer pink, 4 to 5 minutes.
Stir in 28 ounces canned diced tomatoes and 14 ounces tomato sauce. Season with 2 teaspoons dried oregano, 1 1/4 teaspoons kosher salt and 1/4 teaspoon freshly ground black pepper. Simmer for 10 minutes over medium-low.
Meanwhile, in a large bowl, combine 16 ounces ricotta, 8 ounces (2 cups) shredded mozzarella, 2 ounces (3/4 cup) Parmesan, 1 egg, 1/3 cup chopped basil, 1/2 teaspoon kosher salt, and 1/8 teaspoon freshly ground black pepper.
To assemble the lasagna, scoop all but a very thin layer of sauce out of the skillet and into a bowl. Top with 4 to 5 no-boil lasagna noodles, breaking them to fit into an even layer. It doesn’t matter how broken up the noodles are, they will cook into one big noodle layer, so just wedge them into the skillet as best you can!
Top with 1/3 of the ricotta mixture and 1/4 of the remaining tomato mixture. Top with a layer of zucchini noodles, overlapping them and squeezing them into the skillet however necessary to make an even layer across the sauce, and follow the same pattern two more times - once with no-boil noodles, once with a second layer of zucchini noodles.
Cover the top layer of noodles completely with the remaining tomato sauce. If you do not have enough tomato sauce left to cover the noodles at the end, pour 1/4 cup water over top and press down to submerge completely in liquid. It is very important that the no-boil noodles are covered in liquid, otherwise they will not cook. Top with the remaining 1 cup grated mozzarella and 3/4 cup Parmesan cheese.
Tent the skillet with foil so that it is not touching the cheese.
Bake for 40 minutes, then remove foil and broil for an additional 3 to 4 minutes to lightly brown the cheese.
Garnish with basil and freshly ground black pepper.