Warm milk to 90-100℉. Melt butter to 90-100℉. Crack and beat room temperature egg. Combine milk, melted butter, and beaten egg in the bowl of a stand mixer.
Add dry ingredients to mixture: flour, sugar, salt, and yeast. Use dough hook attachment to mix the dough. Alternatively, can knead by hand.
If using a stand mixer, once all of the ingredients are combined, allow the dough hook to knead the dough for 2-3 minutes.
Dough should not stick to fingers when pressed onto it. If dough is sticky add a tbsp of flour. If dough is too dry, add 1 tbsp of water or milk.
Lightly grease a large bowl. Place dough in prepared bowl. Cover with cloth, set in a warm spot, and let rise for 1 hour.
Dough should at least double in size.
When dough has risen, on a clean work surface, use a rolling pin to flatten dough into a 15"x12" rectangle.
To make filling
While dough is rising, in a bowl, combine brown sugar, softened butter, honey, vanilla extract, and ground cinnamon. Mix until all ingredients are well combined.
To make the honey buns
Spread the filling evenly over the flattened dough, leaving 1/2 inch without filling on all sides.
Gently roll dough from the long side into a long tube.
Using a serrated knife, cut tube into 12 honey buns. Each bun will be a little over an inch thick.
Line a 9"x13" casserole dish with parchment paper or grease well.
Place rolls into prepared 9"x13" dish. Cover with a towel and let rolls rise a second time for 30-45 minutes.
Preheat oven to 375℉.
After the second rise, remove towel and place honey buns into preheated oven. Bake for 20 minutes.
Remove from oven and let cool.
To make icing
While rolls are cooling, place softened cream cheese, honey, softened butter and vanilla extract in a bowl. Mix well with a hand mixer until all lumps are smoothed out.
To finish honey buns
Once the buns have cooled for 10-15 minutes, Drizzle icing over the rolls.