Comine the warm milk and yeast in a bowl and let it sit for 10 minutes.

Combine the flour, salt, and sugar in a stand mixer and mix to combine. Add the room temperature butter and mix on medium speed until you achieve the texture of breadcrumbs.

Switch to a dough hook and add the yeast mixture and caraway seeds. Mix on medium speed until it just combined. Let it sit for 10 minutes.

Turn the mixer on to medium speed. Knead the dough for 8 minutes until it forms a very smooth ball of dough and the sides of bowl are clean.

Cover and place the dough in a warm area for 45 minutes or until doubled in size.

Preheat the oven to 375F. Turn the dough out onto a lightly floured surface and divide it into 12 equal size pieces. Roll each piece in balls and push a sugar cube into the seam side of the dough. Pinch to close the seam and roll back into a ball shape.

Place the seam side down on a baking sheet and cover with a damp cloth of plastic wrap. Place it in a warm area for 30 minutes until proofed and doubled in size.

When proofed, brush each bun with the egg and bak for 15-20 minutes until golden brown.