Make the honeydew syrup. Puree 2 cups honeydew until smooth. Combine with ¼ cup sugar and bring to a boil over medium heat in a medium saucepot. Continue to cook until the liquid is reduced by half, about 20 minutes. Remove from heat and cool completely.
Prepare the dough for the bread. Combine 1 teaspoon active dry yeast with 1 teaspoon sugar and ½ cup warm milk. Let sit for 10 minutes or until the yeast has been activated and the mixture is foamy. Mix together the yeast mixture with 1 ¾ cups bread flour, ½ teaspoon salt, 2 tablespoon sugar, 2 tablespoon softened butter, and 1 egg until the dough comes together. Knead the dough for 7-8 minutes or until smooth. Transfer the dough to a clean bowl, cover with plastic wrap, and let rise in a warm area for 1 hour or until doubled in size.
Meanwhile, make the honeydew custard. Puree about 2 cups honeydew to make 1 ½ cups honeydew juice. Whisk together the juice with 4 eggs, ½ cup sugar, 2 tablespoon cornstarch, 1 teaspoon vanilla, and ¼ cup honeydew syrup. Bring to a simmer over medium-low heat in a medium saucepot, whisking continuously. Continue to simmer the custard until it thickens, about 5-7 minutes. Remove from heat and transfer to a clean bowl. Place plastic wrap directly on top of the custard and let cool completely.
Punch down the dough and divide it into 8 even pieces. Shape each piece into a round ball and roll it out into a 6-inch circle. Fill the center of the dough with 2 tablespoon honeydew custard (add more custard if you can!) and gather up the edges to seal in the custard. Place the seam side down on a lined baking sheet and continue with the remaining dough. Loosely wrap the honeydew bread and let rise in a warm area for 1 hour.
Meanwhile, make the bread topping. Cream together 5 tablespoon softened butter with ⅓ cup sugar until light and fluffy, about 2-3 minutes. Add 1 egg and beat until combined. Add 2 tablespoon honeydew syrup, 1 ½ cups cake flour, ½ teaspoon baking powder, and 1 drop of green food coloring if using. Mix well until the green food coloring is well distributed in the dough. Shape the dough into a log and chill in the fridge for at least 30 minutes or until firm.
Preheat oven to 350 degrees F.
Remove the bread topping from the fridge and slice into 8 pieces. Flatten each piece until it's big enough to cover the top of the bread. Lay the bread topping on top of the rolls and score the top, making a crisscross pattern. Bake the honeydew bread for 10-12 minutes or until the bottoms of the bread are browned. Let cool completely. Serve.