Chinese hot dog buns

1. You’ll need:

2. 2/3 cup heavy cream (at room temperature)
1 cup, plus 1 tablespoon milk (at room temperature)
1 large egg (at room temperature)
1/3 cup sugar
1/2 cup cake flour
3 1/2 cups bread flour
1 tablespoon active dry yeast
1 1/2 teaspoons salt
1 tablespoon oil
12 hot dogs
Egg wash: whisk together 1 egg with 1 teaspoon water
Simple syrup: 2 teaspoons of sugar dissolved in 2 teaspoons hot water