In a stand mixer, combine the all-purpose flour, granulated sugar, and salt. Heat the whole milk to 110°F and mix it with the instant yeast, melted butter, egg, and vanilla extract. Slowly pour the wet ingredients into the dry ingredients while mixing on low speed for about 10 minutes, until a soft dough forms that pulls away from the bowl’s sides.

Shape the dough into a ball and place it into a greased bowl, turning it to coat with oil. Cover the bowl with a clean kitchen towel or plastic wrap, and let it rise in a warm, draft-free spot until doubled in size, about 1½ hours.

Once the dough has risen, punch it down gently to remove excess air. Roll it out on a floured surface into a rectangle about ½ inch thick. Sprinkle the ground cinnamon evenly over the surface and roll the dough tightly into a log. Cut the log into 1-inch pieces to create approximately 14 buns.

Arrange the cut dough pieces on a sheet of wax or parchment paper, leaving space between each bun. Cover them lightly with the kitchen towel again and let them rise for another 30 minutes.

Heat the vegetable oil in a deep skillet to 350°F. Carefully add a few dough pieces to the hot oil, making sure not to overcrowd the pan. Fry the buns for 1–2 minutes on each side, or until golden brown.

While the buns cool slightly, prepare the glaze by whisking together melted butter, powdered sugar, additional milk, honey, and a splash of vanilla extract until smooth. Dip the warm honey buns into the glaze, allowing it to coat generously.