In a stand mixer fitted with the dough hook, add in the flour, sugar, and salt.
In a microwave-safe bowl, add in the milk. Microwave for 30 seconds. You'll want the milk to be at 105 - 110 degrees F.
Add in the yeast, cooled melted butter, and egg. Using a fork, whisk the egg into the mixture.
Pour the wet mixture into the stand mixer and mix on medium for 10 minutes. The dough will be pretty sticky.
Grease your hands and a large bowl with vegetable oil.
Remove the dough from the mixer and shape it into a ball.
Place the dough in the bottom of the bowl and coat it in the oil. Cover the bowl with plastic wrap and let the dough rise until doubled. This will take about 1 to 2 hours.
Line a cookie sheet with parchment paper. Spray the parchment paper with nonstick baking spray.
Once the dough has doubled, press it down.
Place the dough on a lightly floured work surface.
Press the dough out into a 6-inch by 14-inch rectangle. You can use a rolling pin, but I prefer to use my hands.
Sprinkle the cinnamon on top of the dough. Using your hand, rub the cinnamon all over the dough.
Begin rolling the dough from the long side.
Once the dough is rolled up, you'll need to seal the edge. Do this by rubbing the edge of the dough with water. Pinch the wet edge into the roll of dough to form the seam. If the dough isn't staying pinched together, rub a little more water on the edge and pinch again. Leave the dough seam side up since it will be sticky from the water and will likely stick to the counter if it touches it.
Measure out 1/2-inch thick slices if you want thinner honey buns or 1-inch slice for thicker slices.
Slide a piece of floss under the dough and cross both sides of the floss at the 1/2-inch or 1-inch line. Pull until the floss has cut completely through the dough.
Place the slice of dough, cut side up, on the prepared cookie sheet. Repeat with the remaining pieces slices of dough. If you plan on baking these, you'll want to space them 2 inches apart. If you plan on frying them, they can be 1/2 inch apart.
Spray the slices with nonstick baking spray so they don't dry out and cover with plastic wrap. Let rise for 30 minutes in a warm place.
Baked Honey Buns
Preheat the oven to 350 degrees F.
Place the cookie sheet in the oven and bake for 15 to 18 minutes until the edges begin to turn golden brown.
Prepare the glaze while the honey buns are baking.
Remove the honey buns from the oven and let cool for 10 to 20 minutes. While they're still warm, dip the tops in the glaze. Tap the wrist that's holding the honey bun to remove the excess glaze.
Place on a piece of wax paper and let the glaze set up.
Fried Honey Buns
Heat 3 cups of vegetable oil until it reaches 320 degrees F.
Prepare the glaze while you wait for the oil to come up to temperature.
Place the honey buns in one or two at a time into the oil. I did one at a time to keep my oil temperature from dropping.
Flip once the donuts become golden brown.
Once the other side becomes golden brown, place on a plate lined with paper towels. Let cool for 5 to 10 minutes.
Dip the warm honey bun in the glaze. Give your wrist a tap to help any excess glaze to drip off.
Place on a piece of wax paper and let the glaze set up.
Glaze
In a medium mixing bowl, add in the butter, powdered sugar, milk, and vanilla extract. Whisk together until the glaze is smooth.