In a stand mixer with a dough hook, combine flour, granulated sugar, and salt.
Heat the milk in a microwave-safe bowl for about 30 seconds until it reaches 110°F.
Add the instant yeast, melted butter, large egg, and vanilla to the warm milk and whisk until combined.
Pour the wet mixture into the stand mixer and knead on medium for about 10 minutes. Make sure all ingredients are mixed well by scraping down the sides.
Grease a large bowl with vegetable oil.
Remove the dough, shape it into a ball, and place it in the oiled bowl. Cover with plastic wrap and let it rise for about 1½ hours, or until it doubles in size.
After rising, press down on the dough gently and transfer it to a floured surface.
Roll the dough into a rectangle of about 15 inches by 8 inches.
Evenly sprinkle with ground cinnamon across the top.
Start from one long side and roll the dough tightly into a log shape. Moisten the edge with water to seal it by pinching the seam.
Cut the dough log into 1-inch pieces using unscented dental floss.
Place the buns on wax paper and lightly spray the tops with cooking spray. Cover with plastic wrap and let rise for an additional 30 minutes.
In a large pan, heat vegetable oil over medium heat.
Fry each bun in hot oil, a couple at a time, turning until golden brown on both sides.
Transfer the fried buns to paper towels to drain excess oil.
While cooling, mix the icing ingredients in a small bowl until smooth.
Dip the warm tops of the buns into the icing, then place them on wax or parchment paper to let the icing set. Enjoy!