Make the cake: Position a rack in the lower third of the oven; preheat to 350 degrees F. Generously coat a 10- to 15-cup Bundt pan with cooking spray. Combine the flour, peanuts and peanut butter powder (if using) in a large bowl. Lightly stir the eggs and egg yolks in a bowl with a fork until they are just streaky; set aside.
Beat the butter in a large bowl with a mixer on medium speed until fluffy, about 2 minutes. Add the granulated sugar, then the brown sugar and beat until fluffy, about 4 minutes. Beat in the peanut oil, vanilla and salt; scrape down the sides of the bowl. Reduce the mixer speed to low and add the beaten eggs in three additions. Beat in the confectioners' sugar and cocoa powder until just combined; do not overmix. Fold in the flour-peanut mixture with a rubber spatula.
Pour the batter into the prepared Bundt pan and spread it evenly. Bake 45 minutes (be careful not to overbake). Transfer to a rack and let cool 20 minutes in the pan. Gently press down on the cake to remove any air bubbles in the tunnel (it's OK if the cake cracks a little bit), then let cool completely in the pan, 3 hours.
Make the glaze: Whisk the confectioners' sugar, milk, peanut butter, vanilla and salt in a medium bowl until smooth. Invert the cake onto a plate and pour the glaze on top.