In a small bowl or measuring cup, stir 1 cup warm milk, 2 tbsp sugar and 2¼ tsp yeast until combined. Let stand until foamy and bubbly (about 10 minutes).
In a large bowl if mixing by hand, or using the bowl of your stand mixer fitted with the dough hook attachment (see notes), stir yeast mixture, 3 cups flour, ¼ cup sugar, ½ tsp salt and 1 egg until combined, the dough sticks together in a ball and becomes smooth and elastic. Add more flour a little at time if your dough is too sticky, but no more than ¼ cup in total.
Take the dough from the bowl and gently shape into a ball. Transfer into another bowl that’s been greased with canola oil. Cover and allow to rise until double in size (about 1 hour).
When ready, punch air out of the dough and turn into a lightly oiled surface.
Divide into 12 equal pieces.
Roll each piece into a ball then flatten no thinner than 2mm.
Place a heaping tablespoonful of pan de coco filing (instructions below), fold dough over filling and pinch to seal. Reshape if needed.
Place each roll, seam side down, on a lightly greased 9x13 inch baking pan and allow to rise a second time (about 30m).
Preheat oven to 350F, brush the pan de coco with egg wash (1 egg combined with 1 tbsp water) and bake for 20 minutes or until the tops are golden brown. Best served warm.
While you're waiting for your dough to rise, you can work on your filling. First, bring 1 cup coconut milk to a simmer.
Add ½ cup brown sugar and stir until dissolved.
Add 1 cup shredded coconut and ½ tsp salt and cook on medium heat until thickened considerably (10-15m). Stir often so it doesn’t burn (see notes). Set aside until you're ready to use.
I've used both sweetened and unsweetened shredded coconut for the filling and didn't notice a significant difference in taste. You can use whatever you have on hand. Or opt for unsweetened if you want to control the sugar content.
When I’m making pan de coco, I start stirring by hand then switch to the dough hook attachment of my stand mixer to finish things up. If you're stirring by hand, once the dough comes together in a ball, turn into a lightly oiled surface and knead until smooth and elastic.
Remember that the coconut filling will thicken as it cools so you don’t want to overdo it. Otherwise, it will get very thick and very hard like candy.