Combine the water, yeast, and a pinch of the sugar in the bowl of your mixer. Let it sit for 5 minutes.
Add in the remaining sugar, salt, milk, butter, eggs, and yolks.
Add the flour.
Knead with the dough hook attachment for five minutes.
The dough should be a smooth ball that has pulled away from the sides of the bowl.
Place the dough in a large bowl that has been sprayed with non-stick spray.
Cover with plastic wrap and let rise in a warm place for 1 hour or until doubled in size.
Place the dough onto a lightly floured work table.
Roll out to ½’’ thick.
Cut out the donut, place on sheet pans, cover with plastic and let rise for another 20–30 minutes or until doubled again.
While the donuts are poofing, preheat your fryer or your oil to 350 degrees Fahrenheit.
Fry the donuts in batches for a few minutes each side or until they are cooked through and a cake tester inserted in the center comes out clean.
Let cool and drip excess oil off on a resting rack as you fry the other batches.
Melt butter and brush on top of the doughnut bagels. Sprinkle with everything bagel seasoning.