Preheat oven to 350 F (180 C). Line the bottom of a tube / angel food cake pan with parchment paper, set aside. (Do not grease the pan)
Separate egg whites into the bowl of a stand mixer, allow to stand at room temperature for about 20 minutes.
In a separate bowl, mix together the pecan meal, flours, starches, baking powder, and xanthan gum; set aside.
Add cream of tartar and salt to the egg whites, use a whisk attachment to bear on low until combined. Turn speed up to high, beat until stiff peaks form. Turn speed down to medium, and slowly add the sugar, a little at a time, until combined. Turn speed to low, add vanilla, mix just until combined.
Remove bowl from stand mixer, gently fold in the flour mixture – about ½ cup at a time – JUST until combined. Be gentle- you don’t want to deflate the eggs!
Gently spoon mixture into tube pan. Bake for 35-40 minutes, or until a knife inserted into the middle of the cake comes out clean.
Invert cake onto a cooling rack – leaving it in the pan – and allow to cool for about an hour. Remove pan, slice cake into 3 equally thick layers.
Whisk 2 cups of the heavy whipping cream together with the icing sugar and vanilla until very thick. Spread as filling between the 3 cake layers, stacking as you go. Use remaining whipped cream to frost the sides and center of the cake, decorate with more pecans as garnish if desired. Chill for at least two hours.
Melt butter in a medium saucepan. Add brown sugar and heavy cream, whisking until smooth. Bring to a boil over medium heat. Boil for 2 minutes, then remove from heat. Stir in vanilla, allow to cool.
To serve, warm the sauce, drizzle over whole torte, and/or individual slices.