Bake the Cake:

1. Preheat oven to 350F. Generously butter a bundt pan, then lightly dust with flour, tapping to shake out the excess.
2. In a large mixing bowl, whisk together the flour, sugar, cocoa, baking powder, baking soda, spices, and salt.
3. In a second bowl, whisk together buttermilk, pumpkin and brown sugar until smooth. Add the whole egg and egg white, and mix until smooth. Add oil, corn syrup, and vanilla. and whisk until smooth.
4. Gently fold the wet ingredients into the dry ingredients, being careful not to overmix (it's okay if there are still a few floury streaks in the batter). Pour into the prepared bundt pan, and smooth out into an even layer.
5. Bake in preheated oven for 1 to 1 1/4 hours, or until a skewer inserted into the middle of the cake comes out with a moist crumb. Let cool in the pan for 15 minutes, then gently remove the cake from the pan and let cool completely on a wire rack, about 2 hours.

Make the Glaze:

1. In a small saucepan set over medium-high heat, melt the butter and cook until golden brown. Remove from heat immediately.
2. In a small mixing bowl, whisk together browned butter, pumpkin puree, cream, vanilla and nutmeg. Sift in the icing sugar, and whisk until smooth. The glaze should be fairly thick, but still pourable. (If it's too thick, add more cream by the teaspoon until it loosens up. If it's too runny, add more icing sugar by the tablespoon until it thickens up.)
3. Immediately pour the warm glaze onto the cooled cake, letting it drape softly over the sides. Let stand for 30 minutes to allow the glaze to set, then serve.