In a large bowl, mix together the bread flour, sugar, yeast, and salt. Set aside.
In another bowl, whisk together the warm water, honey, egg, and vanilla extract until smooth. Add the vegetable oil and mix until fully combined.
Using a stand mixer with a dough hook, combine the wet and dry ingredients. Mix on low until a dough forms, then knead on medium speed for about 8 minutes. The dough will be soft, slightly sticky, and more elastic thanks to the bread flour.
Transfer the dough to a lightly greased bowl, turning it once to coat. Cover and let rise in a warm spot for 1–2 hours, until puffy and nearly doubled.
While it rises, mix together the brown sugar and cinnamon. This will give you a richer, slightly gooier filling compared to white sugar.
Roll the dough into a 12x8-inch rectangle on a floured surface. Sprinkle the cinnamon brown sugar evenly over the dough, leaving a small border. Gently press it in.
Roll tightly into a log, seal the edge with a little water, then slice into 1-inch pieces. Place on a parchment-lined baking sheet, lightly flatten, and let rise for 45 minutes until puffy.
Heat oil to 365°F. Fry each piece for about 90 seconds per side until golden brown.
Transfer to a rack, then dip warm buns into the glaze and let set for that classic slightly crisp finish.