Put the warm water and honey in a mixing bowl, and sprinkle the dry yeast over the surface. Stir to combine, and set aside for 5 minutes or until foam forms on top.
In another bowl, combine the egg with sour cream, sugar, salt, and almond extract, then stir in the water, honey, and yeast mixture.
Add half of the flour and mix until combined. Continue adding the flour, just a few tablespoons at a time, until the dough starts to pull away from the sides of the bowl.
Transfer the dough to a lightly floured surface and knead for a few minutes until the dough has an elastic stretch to it. While kneading, try to not add too much flour, as it will result in a tougher bun.
Use the vegetable oil to grease a big bowl, then transfer the dough into the bowl, cover it with a clean dishtowel and set it in a warm place to rise for 1 hour until doubled in size.
In the meantime, prepare the almond paste filling.In a bowl, add the egg white, almond flour, powdered sugar, almond extract, and a pinch of salt and mix well until you have a creamy paste. Set aside. Punch down the dough, transfer it to a lightly floured surface, roll it and cut it into even parts. Keep the dough covered with the dishtowel, to keep it from drying out. Working with one piece at a time, spread the almond filling, roll the dough into snakes, then coil them. Moisten the tail with your wet fingers to prevent it from unrolling, and press it down on edge in order to make a coiled bun.
Place the buns on a baking sheet lined with baking paper, cover with a clean dishtowel, and let them rise for 30 minutes.Preheat the oven at 180℃ and bake for 15 to 20 minutes or until lightly browned. In the meantime, prepare the glaze. Stir the honey, powdered sugar, and milk together in a bowl and mix well until the glaze becomes smooth. Once the honey buns are done, dip the tops into the glaze and enjoy while warm.