In a small bowl, combine the lukewarm milk, yeast, and 1 teaspoon of sugar. Let it sit for 5-10 minutes until frothy, indicating the yeast is active.

In the bowl of a stand mixer fitted with the dough hook, combine the flour, salt, and ½ cup of sugar. Add the activated yeast mixture. Mix on low speed until a shaggy dough forms.

Increase the speed to medium and knead for about 5-7 minutes, until the dough is smooth and elastic. Place the dough in a lightly oiled bowl, cover with plastic wrap, and let it rise in a warm place for 1-1.5 hours, or until doubled in size.

While the dough is rising, prepare the butter block. Place the cold, cubed butter between two sheets of parchment paper. Using a rolling pin, pound and shape the butter into a rough 6x8 inch rectangle. Chill this butter block in the refrigerator until firm.

Once the dough has risen, turn it out onto a lightly floured surface. Gently punch it down. Roll the dough into a rectangle approximately 12x16 inches.

Place the chilled butter block on one half of the dough rectangle, leaving a small border. Fold the other half of the dough over the butter, like closing a book. Pinch the edges to seal the butter inside.

Gently roll the dough and butter package into a long rectangle, about 8x24 inches. Be careful not to press too hard, or the butter will squeeze out. Fold the dough into thirds, like a letter. This is your first fold. Wrap the dough tightly in plastic wrap and refrigerate for at least 30 minutes.

Repeat the rolling and folding process two more times, refrigerating for at least 30 minutes between each fold. After the final fold and refrigeration, roll the dough into a large rectangle, about 10x20 inches.

Trim the edges to create clean lines. Cut the dough into 8-10 equal triangles. For each triangle, make a small slit at the base and gently stretch the dough outwards before rolling it up from the base to the tip, creating the classic crescent shape.

Place the shaped Gipfeli on baking sheets lined with parchment paper, leaving space between them. Cover loosely with plastic wrap and let them proof at room temperature for about 1-1.5 hours, or until puffy and nearly doubled.

Preheat your oven to 400°F (200°C). In a small bowl, whisk together the beaten egg and 1 tablespoon of milk for the egg wash. Gently brush the tops of the proofed Gipfeli with the egg wash.

Bake for 15-20 minutes, or until deeply golden brown and puffed. Let them cool slightly on a wire rack before serving.