Ube Ensaymada

Ingredients

• 1 pouch or 2 1/4 tsp yeast
• 1/4 cup water
• 1/2 tbsp + 1/4 cup sugar, divided
• 1 cup evaporated milk
• 3 tbsp + 1/2 cup unsalted softened butter, divided
• 1 tsp salt
• 3 cups bread flour plus extra
• 2 large eggs, beaten, divided
• ube jam or halaya for filling
• melted butter for coating
• 1 tbsp milk
• 1/2 cup powdered sugar
• extra sugar for topping
• grated cheese