Preheat oven to 350 F. Prepare a 9.5 or 10-inch bundt pan according to guidelines for the specific pan you own (some need spray/flour, others don’t).
In a large mixing bowl, combine the eggs, sweetener, applesauce, and vanilla. Stir to combine, then add the pumpkin and mix in.
Gently fold in the remaining ingredients, mixing the batter until there are no lumps. Be careful not to overmix, though. Transfer the cake batter to the bundt pan and spread in an even layer.
Bake the cake for 45 minutes uncovered, then remove it from the oven and cover it with foil. Return the pan to the oven and bake for 20 to 30 minutes longer. The bake time will vary depending on which sweetener and pan you use. It is best to insert a knife or skewer into a few spots in the cake and ensure it comes out clean before removing it from the oven.
Allow the cake to rest for about 10 minutes before flipping it out, then allow it to rest for a couple of hours or overnight before decorating and serving.
For the optional glaze, mix the powdered sugar replacement (or real powdered sugar) with vanilla extract and Greek yogurt. Add cinnamon to taste and use 1 teaspoon of water at a time until you reach your desired consistency. Carefully pour it over the cooled cake.