You will also need a candy/fat thermometer for frying the donuts, as well as a 12- to 18-inch pastry bag fitted with a 1/4-inch round tip to fill them.
Game plan: The dough can be made in a stand mixer fitted with a hook attachment if you prefer. Place the yeast and sugar in the stand mixer bowl and proceed with the recipe, mixing at medium speed until the dough comes together and forms a ball that is smooth, shiny, and elastic, about 5 minutes.
When deep-frying the donuts, make sure the oil stays at a constant temperature, adjusting your stove’s heat as necessary.
1Place 2 1/2 cups of flour and the salt in a large bowl and whisk to aerate and combine; set aside. Coat a second large bowl with vegetable oil; set aside.
2Place the yeast and 1 teaspoon of the sugar in a medium bowl. Add the water, stir to combine, and let sit until the mixture is foaming, about 5 minutes.
3Add the remaining 1/4 cup sugar, the egg yolks, milk, and vanilla and whisk to combine. Add this mixture to the reserved flour mixture and stir with a wooden spoon until the dough comes together and begins to form a ball.
4Transfer the dough to a lightly floured work surface. Scatter the butter pieces over the dough and knead until the butter is fully incorporated and the dough is smooth, shiny, and elastic, about 6 to 8 minutes. Add up to 1/4 cup of additional flour as needed if the dough is sticky. Form the dough into a ball, place it in the oiled bowl, and turn it to coat it in the oil. Cover the bowl with plastic wrap or a damp towel and let the dough rise in a warm place until doubled in size, about 1 1/2 to 2 hours. Meanwhile, make the filling.
For the ginger-lime curd filling:
1Fill a medium saucepan with 1 to 2 inches of water and bring it to a simmer over high heat; reduce the heat to low and keep the water at a bare simmer.
2Place all of the ingredients except the butter in a large heatproof bowl and whisk to combine. Set the bowl over, but not touching, the simmering water and whisk constantly until the yolks thicken and the mixture forms ribbons when the whisk is lifted from the bowl, about 7 minutes. (Check to make sure the water hasn’t started boiling by periodically removing the bowl from the saucepan using a potholder or dry towel. If the water is boiling, reduce the heat so the eggs do not curdle.)
3Remove the bowl from the simmering water and whisk in the butter 1 piece at a time, waiting until each piece is completely melted and incorporated before adding the next.
4Set a fine-mesh strainer over a medium bowl. Strain the curd, pressing on the solids and scraping the extra curd clinging to the underside of the strainer into the bowl; discard the solids left in the strainer. Press a sheet of plastic wrap directly onto the surface of the curd to prevent a skin from forming; set aside at room temperature.
1Line a baking sheet with parchment paper; set aside. Punch down the dough, transfer it to a lightly floured work surface, and roll it out until it’s about 1/4 inch thick. Using a 2-1/2-inch round cutter, stamp out as many dough rounds as possible and place them on the prepared baking sheet about 1/4 inch apart. Gather the dough scraps into a ball and roll out and cut again. Discard any remaining dough scraps.
2Cover the dough rounds loosely with plastic wrap or a damp towel. Let them rise in a warm place until puffy and about 1/2 inch thick, about 30 minutes.
3Place the oil in a Dutch oven or a large, heavy-bottomed pot and set it over medium heat until the temperature reaches 365°F on a candy/fat thermometer. Meanwhile, fit a wire rack over a second baking sheet; set aside. Place the sugar in a large bowl; set aside. Transfer the ginger-lime curd to a piping bag fitted with a 1/4-inch round tip; set aside.
4When the oil is ready, add 4 of the dough rounds and fry until golden brown, flipping halfway through, about 2 minutes total. (If air bubbles appear in the donuts, pierce them with the tip of a paring knife.) Using a slotted spoon, remove the donuts to the wire rack. Add 4 more dough rounds to the oil. While these dough rounds are frying, use tongs to transfer the first 4 (still-hot) donuts into the bowl of sugar. Toss to coat in the sugar, then return to the wire rack. Repeat frying and sugarcoating the remaining dough rounds.
5When the donuts are cool enough to handle, use a paring knife to puncture the side of each to form a pocket in the center. Place the tip of the piping bag into the pocket and pipe about 1 heaping teaspoon of curd inside. Serve warm or at room temperature.