Separate egg yolks and egg whites into 2 bowls. Let come to room temperature (approximately 1 hour).
Preheat oven to 350℉
Sift together cake flour, baking powder, cinnamon, ginger and nutmeg. Set bowl aside.
In a large bowl, whisk together egg yolks, 3 Tablespoons granulated sugar, vegetable oil, milk and pumpkin puree. Continue whisking until well combined (approximately 1 minute).
Add cake flour mixture to bowl with pumpkin. Fold dry ingredients into the pumpkin mixture using a rubber spatula. Set bowl aside.
Add cream of tarter to bowl with egg whites.
Using a hand- or stand- mixer fitted with the whisk attachment, begin mixing egg whites on medium speed until they become foamy.
Slowly start adding ¼ cup granulated sugar into bowl with egg whites while the mixer is running. This process will take 1 - 2 minutes.
Increase mixer speed to medium-high and continue whipping until stiff, glossy peaks are reached.
Add ¼ of whipped egg whites to bowl with pumpkin mixture. Stir gently with a rubber spatula.
Add pecans pieces to bowl and stir.
Add half of remaining egg whites to the mixture and fold gently until no white streaks remain.
Add remaining egg whites to the mixture and fold gently until no white streaks remain.
Spoon cake batter into tube pan - note: use an ungreased pan. Carefully smooth the top.
Bake for 45 minutes or until well risen and a toothpick inserted in the center comes out clean. Note: you may also check for doneness by inserting a thermometer into the middle of cake. The cake is done when the internal temperature is 200℉
Remove from oven and immediately invert cake pan over onto a cooling rack. Do not remove the pan.
Let cake cool upside down for 1 hour.
Gently lift pan off the cake. If cake is sticking to pan, run a sharp knife around the inside of pan to release.