For the donuts: In a small saucepan, melt the butter over medium-low heat. Let it cook on low heat, swirling occasionally while it crackles and hisses, until the crackling stops and the milk solids in the butter smell toasty and nutty and have turned golden brown, 3 to 4 minutes. Remove from the stove and let cool to room temperature.
Combine the cake flour, almond flour, baking powder, salt and baking soda in a bowl, whisk together and set aside.
In a mixer with the paddle attachment, beat together the melted butter, granulated sugar and lemon zest. Add the almond extract, whole egg and egg yolk and beat until light and fluffy, 2 to 3 minutes. Add the dry ingredients and buttermilk and mix just until a soft dough forms. Remove onto a piece of plastic wrap, flatten out to a disc, cover and refrigerate for at least 1 hour (or overnight if you want to make the night before and finish in the morning).
Unwrap the dough onto a liberally floured surface and pat out with your hands (or you can use a rolling pin) to 3/4 inch thick. Using a 3- to 4-inch glass or round cutter, punch out as many dough circles as you can and place on a baking sheet. Reroll until all the dough is cut. Using a small bottle cap or a round pastry tip, cut a hole in the center of each donut (you can use these pieces to test the oil or to have as snacks). Cover with plastic wrap and refrigerate for 30 minutes to 1 hour. It is important that the dough is cold when frying (chilled dough is easier to handle and results in a nicer crust with well-defined cracks).
Heat 2 inches of oil in a heavy-bottomed pot to 350 degrees F.
For the glaze: Right before frying the donuts, combine the powdered sugar, buttermilk, almond extract, salt and lemon juice in a medium bowl and whisk until smooth.
When the oil is hot, carefully drop the donuts in the oil (2 to 3 at a time; do not crowd the pot). They will sink to the bottom but pop up after 15 to 20 seconds (don’t disturb them during this time). Fry, flipping frequently, until deep golden brown, 3 to 5 minutes. Remove from the oil onto a rack.
While still warm but cool enough to handle, drop each donut into the glaze, flip to coat the entire thing, then let set on the rack. These are the best right away, but they actually keep pretty well for a day or two because they are very moist.
This recipe has been updated and may differ from what was originally published or broadcast.