In a measuring cup mix together the warm water and yeast. Let sit while you prepare the other ingredients. Instant yeast doesn't need to soak in warm water prior to using, but it does help to dissolve it.
In a mixing bowl whisk together the flour, sugar, salt, and baking powder. Set aside.
Melt the butter in a bowl in the microwave or on the stove top. Blend with the silken tofu, milk, and vanilla. You can whisk it but blending it is best for creating a homogenous mixture.
Pour the liquid mix and the yeast water into the dry mix and fold using a heavy spoon until combined. Turn bowl onto a non-floured work surface and knead the dough until smooth. About 5-10 minutes. It will get a little tough but the dough will slacken as it rests.
Place dough into an oiled plastic, glass, or ceramic bowl. Cover. Let rise for 1-2 hours or until the dough has doubled in size.
When your dough is ready to be used, get ready for cooking and decorating. Heat your cooking oil to 375°F. Any deep frying oil is good for this recipe. You will need at least 2" of oil to cook in. Prepare glaze or ganache. See notes for a chocolate glaze. Place a cooling rack on a baking sheet to put your cooked donuts on. Divide dough in half. Place half the dough back into the covered bowl. Each half makes roughly 8 large donuts, 16 total, but you can make them smaller if preferred.
Roll out to roughly 1/4" thick. Cut into donut shapes. I prefer a square donut, like seen in my blog post, because you don't have scrap dough that needs to be rerolled. See blog for reason why. Make sure to punch or cut a hole in the center of your donut. This hole helps the donut to cook evenly and quickly.
Place the cut and shaped donuts onto a parchment lined baking sheet. Cover with plastic wrap. Repeat with the remaining dough.
Cook 3-4 donuts at a time, depending on how much space you have in your oil. 3-4 minutes on the first side, flip, cook 1-2 minutes on the other side. Place cooked donut on the cooling rack and repeat until all donuts are cooked.
The glaze works best if the donuts have cooled for a few minutes rather than right out of the oil or completely cooled. If they are slightly warm they will connect to the glaze better and cool to room temp together.