In the bowl of a stand mixer, combine yeast, about a teaspoon of the sugar and warm water. Let this stand for about 5 minutes, until the mixture looks creamy. Add milk, the melted butter, egg and sugar to the bowl and stir with wooden spoon until combined.
Add the flour, one cup at a time, stirring well after each addition. Once all the flour has been added, the dough will be shaggy and soft. Attach the dough hook to the stand mixer. Knead the dough on medium-high for about 10 minutes or so, until the dough is smooth and is cleaning the sides of the bowl.
Sprinkle some flour to the dough for easier handling. Shape it into a ball and place it in a lightly floured bowl. Cover it with a clean kitchen towel. Let this rise for 1½ hour, or until doubled in bulk.
Meanwhile, make the honey cream filling (instructions below). Once the dough has risen, punch it down gently and divide to 12 portions. Flatten one portion with your palms until it is about ¼ thick. Scoop about 1 ½ tablespoon of the filling in the center. Pull the edges of the flattened dough over the filling to filling. Twist the ends together to seal the dough, forming a smooth ball.
Repeat with the rest of the portions. Arrange the balls of filled dough in a greased 9x13 inch baking pan that is lined with parchment paper. Let them rise, covered for 40 minutes to 1 hour, until puffy and doubled in size.
Preheat oven to 350 F. To make the egg wash, beat one egg with 1 tbsp milk. Brush the tops of the buns with the egg wash. Bake the honey buns for 15-20 minutes or until the buns are golden.