Butter and flour a 12-cup Bundt pan. Sift together the flour, baking soda, salt, pepper.,spices and nuts and set aside.
In a large mixing bowl or the bowl of a standing mixer, beat the eggs with both sugars until light. Mix in the applesauce, oil and vanilla until smooth.
Using a spatula, fold in the dry ingredients, being careful not to over-mix. Pour the batter into the prepared pan and bake for about 45 minutes, until a cake tester inserted in the center of the cake comes out clean.
Cool the cake for 10 minutes in the pan on a rack before turning it out and cooling completely on the rack. Make sure the cake has cooled completely before you apply the glaze.
Put a piece of foil or paper under the cooling rack to catch any drips before you start the glaze. Put the butter in a medium saucepan with the brown sugar, cream and salt and set over medium heat. Bring to a full rolling boil, stirring constantly. Boil for one minute exactly, and then pull it off the heat.
Let the saucepan cool for a couple of minutes, then add the vanilla extract. Now gradually whisk the powdered sugar into the caramel mix through a sieve until you have a thick, but pourable consistency (you may not need all the sugar). If the mixture seems too thick, just add a splash of cream to thin it out a little. Immediately pour the glaze over the cake, moving slowly and evenly to cover as much surface area as possible. Let the glaze set before serving the cake.