Make the cake: Preheat the oven to 375 degrees F. Coat a 10-inch Bundt pan with cooking spray.
Whisk the almond flour, potato starch, orange zest, cinnamon, ginger and salt in a large bowl; stir in the carrots.
Combine the whole eggs and 1 cup granulated sugar in another large bowl. Beat with a mixer on medium-high speed until pale and thick, about 3 minutes. Gently fold in the carrot mixture.
Put the egg whites in another large bowl and beat with a mixer on medium-high speed until just foamy. Gradually add the remaining 1/4 cup granulated sugar and beat until stiff, glossy peaks form, 6 to 8 more minutes.
Gently fold the beaten egg white mixture into the carrot mixture in 3 additions until just combined. Scrape the batter into the prepared pan. Bake until the cake springs back when pressed and a toothpick inserted into the center comes out clean, 25 to 30 minutes. Transfer to a rack and let cool completely in the pan, then invert onto a platter.
Make the glaze: Whisk the confectioners' sugar, orange juice, vanilla seeds and salt in a bowl. Drizzle over the cake and let set slightly before serving.