In a stand mixer bowl, combine flour, sugar, and salt.

Warm milk to about 110 °F; whisk in yeast, melted butter, egg, and vanilla.

Add wet mixture into dry ingredients and knead with dough hook on medium for about 10 minutes, scraping bowl sides occasionally. Dough will be slightly sticky.

Grease a large bowl with oil; place dough inside, cover with plastic wrap, and let rise 1½ hours or until doubled in size.

Punch down dough and transfer to a floured surface; roll out to roughly 15″ × 8″ rectangle.

Mix cinnamon and sugar; sprinkle evenly over dough and gently press it in.

Roll dough tightly into a log lengthwise. Dip fingers in water and pinch seam closed to seal.

Use unscented floss or a sharp knife to cut log into ~1″ thick slices. Place slices on wax paper, cover loosely with plastic wrap, and let rise another 30 minutes.

Heat oil in a pan over medium-high. Fry buns a few at a time, about 1½–2 minutes per side or until golden. Drain on paper towels.

While buns are still warm, make the glaze: whisk melted butter, powdered sugar, honey, vanilla, and salt. Slowly stir in hot water until thick but pourable.

Dip warm buns in glaze, coating tops and sides, then transfer to a cooling rack over parchment and allow glaze to set, about 20 minutes.