Mourning buns recipe from tartine bakery

Ingredients

• 1 teaspoon sugar
• 1/4 cup warm milk or water (105 degrees)
• One 1/4-ounce package active dry yeast (2 1/2 teaspoons)
• 1/2 cup sifted all-purpose flour
• 1/4 teaspoon salt
• 3 tablespoons sugar
• 1 tablespoon warm milk or water (100 degrees)
• 2 large eggs
• 1 1/2 cups sifted all-purpose flour
• 12 tablespoons (1 1/2 sticks) unsalted butter, softened, plus additional for the bowl
• 2 pounds croissant dough
• 1/2 cup brown sugar
• 1/2 cup white sugar
• Finely grated zest of 2 medium oranges
• 2 tablespoons ground cinnamon
• pinch salt
• 4 ounces (1 stick) butter, melted
• extra white sugar for coating muffin cups and for rolling finished buns