Grate the zucchini and squeeze out the liquid, but don't discard it. Save the liquid in one bowl, 2 tablespoons of zucchini in another, and the rest of the zucchini in another bowl.
In a large bowl, whisk together avocado oil, maple syrup, and the warm milk. Make sure the milk is not too cold or hot, otherwise it will kill the yeast. Mix in the yeast and leave it to bloom for 5-10 minutes. It should look very foamy. Whisk in the zucchini and flax meal, then slowly incorporate 3 ¼ cups whole wheat flour, ¾ cup all purpose flour, salt, and baking powder. When it becomes too thick to whisk, switch to a spatula. Cover the bowl and set aside to rise for 1 hour.
Make the filling: In a small bowl, mix together the 2 tablespoons zucchini, cane sugar, applesauce, cinnamon, and flax meal. Set aside.
Once the dough has about doubled in size, add the remaining whole wheat flour and fold it in. Flour your work space with all purpose flour and transfer your dough there. Keep adding flour until you can roll it around and it doesn't stick to your surface. Knead the dough for about 5 minutes.
Put more flour on your surface and on a rolling pin. Roll out the dough until it is ½" thick, turning the dough occasionally so that it does not stick. Trim the edges so that it is in the shape of a rectangle. Spread the filling evenly across the dough.
Grease 2 9"x11" pans (any similar size works, such as 8" x 8").
Cut the dough before rolling! This will create a better spiral and it is easier to roll. Cut about 1" thick pieces and roll them to create a roll. Place each roll into the prepared pan. Cover and rest for 30 minutes to rise.
Preheat oven to 350 degrees Fahrenheit.
Make the icing: Whisk together powdered sugar, lemon juice, vanilla extract, and 8 teaspoons of the reserved zucchini juice (you can substitute nondairy milk) until it form an icing consistency.
Bake for about 20 minutes.
Remove from oven and pour icing on top and enjoy!