Activate the Yeast: In a large bowl, dissolve the yeast in the warm water. Let it sit for about 5 minutes until frothy, indicating the yeast is active.
Mix Wet Ingredients: Add the sugar, salt, softened butter, milk, and egg to the yeast mixture. Mix well until everything is thoroughly combined.
Add Flour: Gradually add the flour to the wet ingredients, stirring until the dough begins to form.
Knead the Dough: Turn the dough out onto a floured surface and knead for about 8-10 minutes, until it's smooth and elastic. Add a little more flour if the dough is too sticky, but try to add as little as possible to keep the dough soft.
First Rise: Place the kneaded dough in a greased bowl, turning once to grease the top. Cover with a clean kitchen towel and let it rise in a warm, draft-free place for about 1 to 1 1/2 hours, or until doubled in size.
Shape the Crescents: Once risen, punch down the dough gently and turn it out onto a floured surface. Divide the dough in half, and roll each half into a circle about 1/4 inch thick. Cut each circle into 8 wedges. Roll up the wedges starting from the wide end to form crescents.
Second Rise: Place the shaped crescents on a baking sheet lined with parchment paper, making sure the tip is tucked under each roll to prevent unrolling during baking. Cover and let them rise again for about 30 minutes, or until nearly doubled.
Preheat the Oven: While the crescents are rising, preheat your oven to 375°F (190°C).
Bake: Brush the tops of the crescents with melted butter, then bake in the preheated oven for 12-15 minutes, or until golden brown.
Cool and Serve: Remove from the oven and place on a wire rack to cool slightly. Serve warm for the best taste.