Bring a pot of water to a boil over medium heat, and cook the zucchini until tender, about 5 minutes.
Drain the zucchini in a colander set in the sink, and set aside to cool.
Preheat oven to 350 degrees F (175 degrees C). Grease a 9x13-inch baking dish.
Combine 1 cup of flour, 1/2 cup of sugar, and 1/2 cup of very soft butter in a bowl until crumbly and well combined. Press the mixture into the bottom of the prepared baking dish.
Measure out 3 cups of cooked zucchini, and place into a blender.
Pour in the evaporated milk and eggs, and add 1 1/2 cups of sugar, 1/4 cup of flour, 1 tablespoon of butter, and the vanilla extract to the zucchini. Pulse the blender several times to combine the ingredients, and then blend until the filling mixture is pureed, about 1 minute.
Pour the mixture over the crust.
Combine 1 tablespoon of sugar with the cinnamon in a small bowl, and sprinkle over the filling.
Bake in the preheated oven until the middle of the dessert is set, about 45 minutes.
Let cool, and chill in refrigerator before slicing.