In a small bowl, dissolve the sugar in warm water. Sprinkle the yeast on top and let it sit for about 5-10 minutes until foamy.
In a large mixing bowl, combine the flour and salt. Cut in the butter until the mixture resembles coarse crumbs.
Add the yeast mixture, milk, and egg to the flour mixture. Stir until a dough forms.
Turn the dough onto a floured surface and knead for about 5-7 minutes, or until smooth and elastic. Place the dough in a lightly oiled bowl, cover with a damp cloth, and let it rise in a warm place for about 1 hour, or until doubled in size.
Once the dough has risen, turn it onto a floured surface and divide it into 2 equal portions. Roll each portion into a circle about 1/4 inch thick.
Cut each circle into 8 wedges. Roll each wedge from the wide end to the point to form crescent shapes.
Place the crescent rolls on a baking sheet lined with parchment paper. Cover with a cloth and let them rise for about 30 minutes.
Preheat the oven to 375°F (190°C). Brush the rolls with the beaten egg and sprinkle with caraway seeds or coarse salt if desired.
Bake for 15-20 minutes, or until golden brown.
Allow the rolls to cool slightly on a wire rack before serving.
Enjoy your meal!