In the bowl of a stand mixer, combine bread flour, sugar, salt, and instant yeast.

Add the eggs, finely grated lemon zest, and cold water to the bowl.

Using the dough hook, mix on low speed (setting 2) for 3-4 minutes until a shaggy dough forms and no dry flour remains.

Increase to medium speed (setting 4) and mix for 6-8 minutes until the dough is smooth, pulls away from the sides of the bowl, and starts to climb the hook.

Stop the mixer and let the dough rest for 5 minutes. This relaxes the gluten and gives the mixer a break.

With the mixer running on medium-low speed (setting 3), add the softened butter a few pieces at a time.

Wait until each addition is mostly incorporated before adding more. This takes 5-8 minutes total.

Once all butter is added, increase to medium-high speed (setting 6) and mix for another 4-5 minutes.

The dough is ready when it is glossy, smooth, and very elastic; it pulls away cleanly from the sides and bottom of the bowl; it makes a slapping sound against the bowl; and it passes the windowpane test.

Transfer the dough to a lightly greased bowl or container.

Cover tightly with plastic wrap.

Let rise at room temperature (70-75°F / 21-24°C) for 1.5-2 hours, until doubled in size and puffy.

Gently press down on the dough to deflate it.

Re-cover tightly with plastic wrap, pressing it directly onto the surface of the dough to prevent a skin from forming.

Refrigerate for at least 8 hours or up to 24 hours.

Line two baking sheets with parchment paper and dust lightly with flour.

Remove the dough from the refrigerator. It will be firm and easy to work with.

Turn the dough onto a lightly floured surface.

Using a bench scraper and kitchen scale, divide the dough into 20 pieces (about 50g each).

To shape each doughnut: cup your hand over a piece of dough, roll it in a circular motion against the counter applying gentle pressure. The friction will pull the dough into a tight, smooth ball.

Place seam-side down on the prepared baking sheet, spacing doughnuts at least 2 inches apart.

Cover the baking sheets loosely with plastic wrap or a clean kitchen towel.

Let the doughnuts proof at room temperature (70-75°F / 21-24°C) for 3-4 hours.

The doughnuts are ready when they have doubled in size, look puffy and pillowy, a gentle poke test|poke leaves an indent that slowly springs back, and they jiggle slightly when you shake the pan.

Fill a deep-fat fryer, Dutch oven, or heavy pot with oil to a depth of at least 3 inches. The oil should not fill the pot more than halfway.

Heat the oil to 350°F (175°C). Use a thermometer—this is critical.

Set up a wire rack over a baking sheet for draining. Place the sugar for tossing in a wide, shallow bowl.

Working in batches of 2-3 doughnuts at a time, use a floured bench scraper to gently lift each doughnut from the pan. Handle them delicately to avoid deflating.

Carefully lower into the hot oil, top-side down.

Fry for 1.5-2 minutes on the first side until deep golden brown.

After about 1 minute, gently press down on any doughnuts that are floating high. This ensures even browning.

Flip using a spider strainer or slotted spoon.

Fry for another 1.5-2 minutes on the second side.

Remove to the wire rack to drain for 30-60 seconds.

Check the oil temperature between batches. Adjust the heat as needed to maintain 350°F (175°C).

While the doughnuts are still warm (but not so hot they'll burn you), toss them in the sugar bowl. Roll to coat all sides generously.

Transfer to a clean wire rack and let cool for at least 15-20 minutes before filling.

Use a chopstick, skewer, or paring knife to poke a hole in the side of each doughnut. Wiggle gently to create a small pocket inside.

Fit a piping bag with a round tip (or use a zip-top bag with the corner cut off).

Insert the tip into the hole. Squeeze gently until you feel the doughnut become heavier and see the filling just start to peek out.

About 2-3 tablespoons of filling per doughnut.

Fill pot with 3 inches of neutral oil. Heat to 350°F (175°C).

Carefully lower doughnuts into oil. Fry 1.5-2 minutes until golden.

Flip with spider strainer. Fry another 1.5-2 minutes.

Remove to wire rack. Drain 30-60 seconds before sugaring.

Bake at 375°F (190°C) for 12-15 minutes until golden and internal temp reaches 190°F.