In the bowl of a stand mixer fitted with the paddle attachment, beat sugars and eggs at medium speed until lightened in color and well combined, 2 to 3 minutes, stopping to scrape sides of bowl. Add melted butter, vanilla, and lemon zest; beat until well combined, about 1 minute.

In a medium bowl, whisk together flours, baking powder, and salt. With mixer on low speed, add flour mixture to sugar mixture alternately with buttermilk, beginning and ending with flour mixture, beating just until smooth and combined after each addition, stopping to scrape sides of bowl. Place in another medium bowl; cover and refrigerate overnight.

In a 5½ -quart enamel-coated cast-iron Dutch oven, melt shortening with oil over medium heat; heat until a deep-fry thermometer registers 365°F (185°C). Line a large rimmed baking sheet with paper towels.

On a heavily floured piece of parchment paper, roll or pat dough into a 9-inch square (about ½-inch thickness), flouring rolling pin or hands as needed. Using a floured chef’s knife, cut dough into 3-inch columns, separating as you cut them. (Columns will start sticking back together if not separated.) Place 1 column on a heavily floured surface. (Refrigerate remaining columns on a piece of parchment paper.) Cut column into 3x1½-inch rectangles. Using the tip of the floured knife, score lengthwise down center of each rectangle, making sure not to cut all the way through.

Using a fish spatula, lift dough rectangles, one at a time, and place, scored side up, in hot oil. (If dough turns in the oil, use spatula to turn it back over.) Working in batches*, fry doughnuts until deep golden brown, 1½ to 2 minutes per side. Remove from oil, and let drain on prepared pan. Repeat cutting and frying with remaining dough.

Dip tops of doughnuts into Lemon Glaze, letting excess drip off. Place on a wire rack, and let stand until glaze dries. Serve warm or at room temperature.