In the bowl of a stand mixer fitted with the paddle attachment, mix warm water, yeast, and 1 teaspoon of sugar. Let it sit for about 10 minutes until foamy.
Add the eggs, remaining sugar, and flour to the bowl. Switch to the dough hook attachment and mix on low speed until a shaggy dough forms.
4 large eggs, ½ cup granulated sugar + 1 tsp, 4 ½ cups bread flour or all-purpose flour
Knead on low speed for 4 minutes. Add the softened butter and continue kneading for another 6 minutes until the dough is smooth, stretchy, and slightly sticky. To check if it's ready, perform the windowpane test—take a small piece of dough and gently stretch it between your fingers. If it becomes thin enough to see light through without tearing, it’s ready.
½ cup salted butter
Transfer the dough to a greased bowl, cover it, and refrigerate for 8 to 12 hours (overnight is best).
The next day, roll the dough out on a lightly floured surface to ½-inch thickness. Cut out donuts using a donut cutter and place them on greased parchment paper. Instead of re-rolling scraps, twist them into crullers. This dough doesn’t do well if you roll it out multiple times, so suggest making the donut balls and the crullers
Cover and let the donuts rise at room temperature until puffy, about 30 minutes to 1 hour.
Heat oil in a deep pot to 350°F. Fry the donuts in batches for 1 to 2 minutes per side, flipping with wooden chopsticks or tongs. Drain on a paper towel-lined wire rack.
2 cups lard or canola oil
While the donuts cool, whisk together powdered sugar, salt, vanilla, melted butter, hot water, and corn syrup in a large bowl until smooth.
Dip each donut into the glaze, coating both sides. Let the excess drip off on a cooling rack and allow the glaze to set completely before enjoying.
Notes
Yeast Activation: If your yeast doesn’t foam after 10 minutes, your water may have been too hot or too cold, or your yeast might be expired. Try again with fresh yeast and water between 100-110°F.
Butter Incorporation: Add the softened butter a few pieces at a time, letting it fully mix in before adding more. The dough may look greasy at first but will come together as you knead.
Second Proofing: The doughnuts are ready when they look slightly puffed and a gentle poke with your finger leaves a slight indentation that slowly springs back.
Frying Temperature: Maintain the oil temperature at 350°F—if it drops too low, the doughnuts will absorb too much oil and be greasy; if too high, they’ll brown too quickly before cooking through.
Glazing Tip: For an extra-thick glaze, let the first layer set for a minute, then dip the doughnuts a second time.