In a small bowl, combine warm milk and 1 teaspoon of sugar. Sprinkle the yeast on top and let it sit for 5 minutes until frothy.

In a large mixing bowl, whisk together the flour, remaining sugar (reserve 2 tablespoons for topping later), and salt.

Pour the yeast mixture and eggs into the dry ingredients. Mix until a shaggy dough forms.

Knead the dough on a floured surface or using a stand mixer. Gradually add the 1/2 cup of softened unsalted butter piece by piece while kneading, continuing until the dough is smooth and elastic (about 10 minutes).

Place the dough in a greased bowl, cover with a cloth, and let it rise in a warm area for about 1 hour, or until doubled in size.

Punch the dough down gently to release air. Divide the dough into 8 equal portions.

Roll each portion into a long, thin rope (about 12 inches long), then coil the rope into a spiral shape like a snail shell, tucking the end underneath.

Place the coiled buns on a baking sheet lined with parchment paper, leaving space between them. Cover and let rise again for 30-45 minutes until puffy.

Preheat your oven to 350°F (175°C).

Bake the buns for 15-20 minutes, or until they are golden brown on top.

Remove from the oven and allow them to cool on a wire rack for 10 minutes.

Ideally while still slightly warm, brush the tops generously with the 1/4 cup softened salted butter.

Sprinkle the tops with the reserved sugar and finish by covering each bun with a generous mound of grated cheddar cheese.