• In a small saucepan, bring the water, milk, unsalted butter, sugar, and salt to a simmer on medium heat.

  Add the flour and sourdough discard, then reduce the heat to low.

  Stir constantly with a spatula or wooden spoon for 2–3 minutes, until the dough forms a thick paste and leaves a thin film on the bottom of the saucepan.

  Transfer the dough to a large bowl if using an electric hand mixer, or to the bowl of a stand mixer, and let it cool for a few minutes before mixing in the eggs.
  100 g Water, 85 g Unsalted Butter, 1 TBS Granulated Sugar, ½ tsp Kosher Salt, 1 tsp Vanilla Extract, 120 g All-purpose flour, 120 g Sourdough Discard, 100 g Whole Milk
• Once the dough has cooled for a few minutes, beat in the egg white and then one whole egg at a time on medium speed, mixing until each is fully incorporated before adding the next. If using a stand mixer, use the paddle attachment.

  At first, the mixture will look loose and separated, but it will gradually come together into a smooth dough. It may appear broken at first, which is normal.

  After beating in the second egg, the dough should be glossy and thick.

  Test whether it needs the third egg (I usually do, since the dough can be quite thick). The dough is ready when it slowly falls from a spatula in a V shape, or when it leaves distinct tine marks that hold their shape after scraping the surface with a fork. If the dough is still too thick, beat in the third egg until fully incorporated.

  The finished choux pastry should be smooth, glossy, and thick enough to hold its shape when piped.
  3 Eggs, 1 Egg White
At this point you can refrigerate the dough to fry later.
• Cut parchment paper into 5-inch squares and lightly grease each one for piping the crullers.

  Transfer the choux pastry to a large piping bag fitted with a large open star tip.

  Pipe the dough into rings about 3½–4 inches in diameter. Let the piped rings rest at room temperature while you heat the frying oil.
• Heat 3 inches of frying oil in a large, heavy-bottomed pot to 365–370°F (185–188°C).

  Place a wire rack lined with paper towels on a sheet pan next to the pot.

  Wear heat-resistant gloves for added protection while frying. Once the oil reaches temperature, use a slotted spoon or spatula to carefully lower a few crullers into the oil, parchment-side up (piped side down). As they fry, the parchment paper will naturally release. Remove and discard it with tongs.

  Fry the crullers in a few batches to avoid overcrowding the pot and to help maintain the oil temperature. Fry for about 2 minutes per side, turning with tongs or a spatula, until the crullers are crisp and golden brown.

  Carefully transfer the fried crullers to the prepared wire rack to drain any excess oil. Check the oil temperature between batches, allowing it to return to 365–370°F if needed before frying the remaining crullers.
  Neutral Oil

Make the Vanilla Glaze

• While the crullers are still warm, mix the powdered sugar, water, and vanilla extract in a bowl.

  The glaze should be thinner and runnier than an icing.
  100 g Powdered Sugar, 1 TBS Whole Milk, ½ tsp Vanilla Extract
• Dip the warm crullers into the bowl of glaze, then return them to the wire rack to cool to room temperature.

  The glaze should set slightly after about 10 minutes. Crullers are best enjoyed warm on the day they’re made!