"This is a recipe that I got from an old friend and then changed just a bit to fit our family. My father-in-law used to make it with white/patty-pan squash, but I have used many kinds: zucchini, white, yellow crookneck, spaghetti squash, and even pumpkin, all with great results, even sometimes mixing two squashes. Most people trying this would not believe it is squash. Enjoy! Serve warm."
Place a steamer insert into a saucepan and fill with water to just below the bottom of the steamer. Bring water to a boil. Add squash chunks, cover, and steam until tender, 10 to 20 minutes. Transfer squash to food processor and blend until pureed.
Stir cornstarch and salt into squash puree. Beat evaporated milk, 1/4 cup sugar, egg yolks, vanilla extract, and ground nutmeg together in a separate bowl. Mix milk mixture into squash mixture. Pour squash mixture into a 9-inch square baking dish.
Bake in the preheated oven until custard is set, about 40 minutes.
Beat egg whites and cream of tartar together in a large glass bowl until foamy. Gradually beat 3 tablespoons sugar into egg mixture until meringue forms stiff peaks. Spread meringue over custard and bake until golden, about 5 minutes more.