MAKE THE ROLLS:

1. COMBINE DRY INGREDIENTS: In a large bowl, combine 2 cups of the flour (reserve the other 2 1/2 cups of flour), the yeast, the granulated sugar, cardamon, and the salt in a bowl. Mix to combine.
2. WARM THE MILK AND BUTTER: In a microwave-safe bowl, microwave the milk and butter for 30 seconds until the milk is warm and the butter is mostly melted. The mixture should be warm (100-110 degrees F) but not hot. If the mixture is too hot, it will kill the yeast and prevent your dough from rising. You can also do this in a saucepan on the stovetop.
3. COMBINE: Add the warm milk and butter to the flour mixture. And then add 1 egg (the other egg will be used as an egg wash for the rolls). Beat on low speed, gradually increasing to high until thoroughly combined. Scrape down the bowl and add 2 1/2 more cups of flour, a little at a time, until the dough starts to pull away from the sides of the bowl and form a ball.
4. KNEAD THE DOUGH: Using your stand mixer fitted with a dough hook, knead at a low speed for about 10 minutes until smooth, and you can stretch a piece of dough out between your fingers without it breaking. This is called the windowpane test, and it determines if the gluten has sufficiently developed. You can also knead the dough by hand on a well-floured surface, but it might take a bit longer.
5. LET DOUGH RISE: Transfer the dough to a lightly oiled bowl, cover the bowl loosely with plastic wrap or a kitchen towel and place the bowl in a warm location. Let the dough rise until it has doubled in size, about an hour. If using regular yeast, it could take 2 hours to rise.
6. FORM THE ROLLS: When the dough is ready, transfer it to a floured surface and knead it for about 2-3 minutes. Divide the dough into 10 equal pieces and then, using your hands, roll each piece into a ball. Place the balls onto a parchment-lined or buttered large baking sheet leaving space between the balls for the dough to rise (like you’re making cookies).
7. LET RISE AGAIN: Cover and let rise for 45 minutes. 
8. PREHEAT THE OVEN: Heat the oven to 350 degrees F. 
9. FILL THE ROLLS: Use your thumb to create a dip in the center of the top of each roll. Fill each with 1-2 teaspoons of vanilla pastry cream. In a small bowl, whisk the remaining egg to make an egg wash. And then, brush the tops of each roll with the egg wash, avoiding the custard center.
10. BAKE THE ROLLS: Bake each sweet bun until the rolls are cooked through, and the tops are golden brown, about 15-18 minutes. And then let the buns cool on a wire rack before frosting.
11. FROST: Once the rolls are cooled to room temperature, spoon the tops with the vanilla icing and then sprinkle with coconut. Again, avoid the custard area. Serve immediately.

MAKE THE VANILLA PASTRY CREAM:

1. COMBINE: While the rolls are rising, make the vanilla custard. To start, take 1 1/2 tablespoons of the milk and whisk it together with the cornstarch in a small bowl. Add the egg and whisk until thoroughly combined. Set aside.
2. HEAT THE MILK, CREAM AND VANILLA: Add the remaining milk, the cream, and the sugar to a small saucepan. Cut the vanilla bean in half lengthwise and scrape out then the seeds with a knife or spoon. Add the seeds to the milk mixture and warm over medium heat to a simmer (don’t boil).
3. WHISK IN EGG MIXTURE: Remove the milk mixture from the heat and slowly whisk it into the egg mixture. Go slow and keep whisking the entire time — you don’t want to scramble the eggs!
4. STRAIN THE MIXTURE: Once it’s combined, strain the mixture back into the saucepan through a fine-mesh sieve to remove any lumps. And then return the pan to the stove and bring it to a simmer.
5. COOK: Simmer the mxiture, while continuing to stir it, until it thickens, about 5 minutes. Don’t boil it. Once done, spoon the pastry cream into a small bowl and let cool before using.

MAKE THE VANILLA GLAZE:

• Whisk together the confectioners’ sugar, milk, and vanilla extract until you get a thick glaze that you can easily spoon on top of the rolls. If it’s too thick, add a tad more milk. If it’s too thin, add a bit more sugar.
• Set aside until ready to use.