Mix flaxseed gel:

In a small bowl, stir together the golden flaxseed meal and water until thoroughly combined. Allow to sit for 5–10 minutes until thickened.

Whisk dry ingredients:

In a large bowl, whisk together the flour, baking powder, instant yeast, sugar, and salt until evenly distributed.

Warm milk and butter:

Combine the milk and melted butter in a microwave-safe bowl. Heat in 30-second bursts until the mixture reaches approximately 110°F (45°C), which typically takes about 1 minute. The liquid should feel warm like baby bath water, not hot; using a kitchen thermometer is advised.

Combine wet and dry:

Create a well in the center of the dry ingredients. Pour in the warmed milk-butter mixture and the flaxseed mixture. Stir on low speed until just combined.

Knead the dough:

If using a stand mixer, attach the dough hook and knead on medium speed until a soft, smooth ball forms, about 5–8 minutes. For hand kneading, work the dough for approximately 10 minutes. If the dough is too sticky, add flour 1 tablespoon at a time until it pulls away from the bowl sides; avoid over-flouring—the dough should remain slightly tacky.

First rise:

Lightly coat a clean bowl with cooking spray and transfer the dough into it. Cover with plastic wrap or a clean kitchen towel. Let it rise in a warm spot for 1.5–2 hours until puffy and doubled in volume. Alternatively, refrigerate for 8–12 hours; an overnight cold rise yields fluffier donuts.

Deflate dough:

After the first rise, turn the dough out onto a floured surface. Gently knead to release trapped air.

Roll and cut donuts:

With a rolling pin, roll the dough to 1/2-inch thickness. Using a 3–3.5-inch doughnut cutter, cut out 6 donuts. If necessary, gather and re-roll scraps once to cut additional donuts. Without a doughnut cutter, use a 3-inch round cookie cutter for the outer shape and a 1-inch cutter for the holes; retain the holes.

Place on parchment:

Place each cut donut and hole on individual pieces of parchment or waxed paper, then set them on a cookie sheet. This step is optional but facilitates handling after the second rise.

Second rise:

Loosely cover with a clean kitchen towel and let rise for 30–45 minutes until slightly puffed. If your kitchen is cool, preheat the oven to 200°F (95°C), turn it off, then place the sheet inside with the door slightly ajar to create a warm environment.

Heat oil:

About 20 minutes before the second rise ends, pour oil into a heavy-bottomed pot or Dutch oven and heat over medium flame to 350°F (175°C). Also, line a large baking sheet or plate with paper towels.

Fry donuts:

Gently lower donuts into the hot oil, two at a time. Once the bottoms turn deep golden brown, after 45 seconds to 1 minute, flip using a slotted spoon and cook until evenly deep golden. Transfer to the paper-towel-lined plate. Repeat with remaining donuts, adjusting heat to maintain 350°F (175°C). Use a frying thermometer; if the oil is too hot, the exterior will brown before the interior cooks.

Make glaze:

Whisk together all glaze ingredients until smooth.

Glaze donuts:

Dip each warm donut into the glaze, coating both sides. Place on a cooling rack to allow excess glaze to drip off. After a few minutes, the glaze will set. Serve right away.