In the bowl of a stand mixer fitted with the dough hook attachment, add the warm water and yeast and stir to combine. Allow to sit for 3 to 5 minutes, or until bubbly.
Add the dry ingredients: flour, cane sugar, and sea salt.
Next, add in the melted butter, and eggs in that order. Mix on low on speed 2 for 3 to 5 minutes, until the dough is smooth.
Transfer to a bowl and cover with plastic wrap. Let rise at room temperature for 1 to 3 hours, until doubled in size. It helps to keep it in a warm place.
Line a baking sheet with parchment paper. Divide the dough into 9 portions, about 90 grams each. Form each of the dough balls into a round ball by tucking the dough underneath.
Place the shaped buns on the prepared baking sheet and cover with a kitchen towel (use plastic wrap if you are in a dry climate). Let rise for 1 hour, or until the dough feels springy.
Preheat the oven to 400°F. Add the milk into a small dish and brush over the tops of the buns.
Bake for 15 to 20 minutes or until golden brown.
Store in an airtight container in the fridge for up to 5 days.