Warm the milk to about 105–110°F. In a small bowl, mix the warm milk, honey, and yeast. Let it sit for 5–10 minutes until foamy.
In a large mixing bowl, combine flour, sugar, and salt.
Add the yeast mixture, egg, and melted butter to the dry ingredients. Mix until a soft dough forms.
Knead the dough for 8–10 minutes until smooth and elastic.
Place the dough in a greased bowl, cover, and let it rise for 1 hour or until doubled in size.
In a small bowl, mix brown sugar, cinnamon, softened butter, and honey to make the filling.
Roll the dough into a rectangle about ¼ inch thick.
Spread the cinnamon honey filling evenly over the dough.
Roll the dough tightly into a log and slice into 1½-inch pieces.
Place the buns on a baking sheet and allow them to rise again for 20–30 minutes.
Bake at 350°F (175°C) for 15–18 minutes until lightly golden.
While the buns cool slightly, whisk together powdered sugar, milk, honey, and vanilla extract to make the glaze.
Drizzle the glaze over the warm honey buns before serving.