Mix the flour, yeast, sugar, and salt in a large bowl on medium/low speed. If you have an electric mixer, you may use that.
Slowly add the warm water. Stir in just enough water for your dough to form a ball and clean the bottom of the bowl.
Knead the dough on medium/low speed for roughly 10 minutes. While it is kneading slowly incorporate the extra 3/4 cup (3 ¾oz/105g) of flour until your dough is smooth and elastic. Try working in as much flour as possible to form a firm but stiff dough. Add a few drops of water if needed to incorporate more flour.
Lightly brush a large bowl with oil and turn the dough to coat. Cover the bowl tightly with cling wrap and a dishtowel. Let rise in a warm place for 1-2 hours - until the dough has doubled in size.
Once doubled, punch the dough down and carefully divide the dough into 16-24 pieces (depends on size of hot dogs)
Get 2 large cookie sheets, and line with parchment paper. Grease (or PAM / oil) parchment paper lightly - this is to help prevent the hot dogs dough from sticking. Note that you can skip the parchment paper, if you wish, and simply grease the pans directly - but I'd recommend using the parchment paper, because of the egg wash step.
Roll the first piece into a thin strip about 16-20 inches long long. Lay hotdog on single strip at about a 45° angle. Roll hot dog along the strip so that it wraps evenly around the hot dog. Note that you should make sure that the ends are wrapped underneath the rest of the strip, so that they don't become unraveled when they are boiled.
Place dough seam side down on parchment paper and repeat until all dogs are rolled. Cover with a towel and let rest 10 minutes.
Bring a large pot of water to boil. Season water with honey and kosher salt. While this is happening, preheat your oven to 375°. Place about 3-4 bagel dogs at a time in boiling water (depending on size of pot). Boil for 1-2 minutes, nudging them slightly to make sure that all sides are boiled as evenly as possible.
After boiling, carefully remove with wire basket or large slotted spoon, removing as much water as possible, then place on the cookie sheets / parchment paper.
Brush the wrapped dogs on both sides (top and bottom) with egg white wash and (optionally) sprinkle with kosher saker.
Place in center of oven and bake for 20-25 minutes, until the bagels are golden brown. Remove from oven and let cool 5 minutes before serving.