This cake is for all those pecan pie lovers who find pecan pie a little too rich or sweet. Chiffon cakes are similar to angel food but use whole eggs rather than whites and usually have some oil to enrich them.
Position a rack in the lower third of the oven and preheat to 325˚ F. Separate the eggs; put the whites in one large bowl and the yolks in another. Let stand at room temperature to warm up while you assemble all the other ingredients, about 30 minutes. (Be prepared to make the cake batter without stopping so the eggs don’t deflate.)
Add the cream of tartar to the egg whites and beat with a mixer on medium speed until thickened and starting to turn white, 1 to 2 minutes. Gradually beat in 1/2 cup granulated sugar, then increase the speed to medium high and beat until the egg whites are glossy, thick and hold stiff peaks but are not dry, about 5 more minutes. Set aside while making the rest of the batter (don’t do this ahead of time or the egg whites will deflate).
Add the remaining 1/2 cup granulated sugar to the egg yolks along with the brown sugar. Beat with the mixer (no need to wash the beaters) until smooth and lightened in color, about 2 minutes. Beat in the vegetable oil and vanilla until smooth and thick, then beat in the milk (the batter will be thin). Add the flour, ground pecans, baking powder and salt and beat on low speed until thoroughly combined.
Add about one-third of the beaten egg whites to the batter and fold in with a rubber spatula until combined. Add the remaining egg whites and continue to fold until no white streaks remain. Pour into an ungreased 10-inch tube pan or angel food cake pan and run the spatula around the center of the batter to create a line where excess air can escape as the cake rises.
Bake the cake until the top is golden and springs back when touched and a long skewer inserted into the center comes out clean, about 1 hour. Remove from the oven and immediately turn the cake upside down over the slim neck of a bottle (if your pan has feet, use those instead). Let cool completely. Use a thin spatula to loosen the cake around the sides and middle of the pan. Turn out onto a platter.
Make the glaze: Melt the butter in a medium saucepan over medium heat. Add the pecans and cook, stirring, until lightly toasted, 2 to 3 minutes. Add the brown sugar, heavy cream, corn syrup and salt and carefully stir to combine. Continue to cook, stirring, until the sauce thickens slightly and starts to pull away from the sides of the pan when stirring, about 5 minutes. Set aside to cool and thicken, stirring occasionally, about 20 minutes.
When the glaze has thickened but is still pourable, spoon it over the cake, letting it drip down the sides. As the glaze cools, use the spoon or spatula to spread some of the pecans that fell down onto the top and sides. Let stand, at least 30 minutes.