In a small bowl, dissolve the yeast and 1 teaspoon of sugar in the warm water. Let it sit for 5-10 minutes until foamy.

In a large mixing bowl, combine the flour, remaining sugar, and salt. Make a well in the center.

Pour the yeast mixture, warm milk, and egg yolks into the well. Mix until a rough dough forms.

Add the softened butter gradually while kneading. Knead on a floured surface or with a stand mixer for about 10 minutes until the dough is smooth and elastic.

Place the dough in a greased bowl, cover with a cloth, and let it rise in a warm place for about 60-90 minutes, or until doubled in size.

Punch down the risen dough and divide it into 8 equal portions.

Roll each portion into a thin rectangle (approx. 4x8 inches). Spread a tablespoon of Ube Halaya evenly over the surface.

Roll the dough up tightly into a long log, then coil the log into a spiral snail shape, 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.

Preheat your oven to 350°F (175°C).

Bake the ensaimadas for 18-20 minutes, or until golden brown.

Remove from oven and immediately brush the tops generously with melted butter.

Sprinkle with extra sugar (optional) and top generously with shredded cheddar cheese while still warm. Serve immediately.