Milk Buns with Salted Maple Butter

Directions

1. Make the tangzhong: In a medium saucepan, combine the flour and milk. Place it over medium heat and whisk until thickened and reaches at least 150ºF on a kitchen thermometer, 2 to 3 minutes. At 150ºF the starches gelatinize. If it turns into a glue-like texture that doesn’t really thicken all that much start again–this means too much of the liquid has evaporated.
2. Make the dough: Transfer the tangzhong to the bowl of a stand mixer with the dough attachment, then add the yeast, milk, sugar, butter, egg, salt, and 2 ¾ cups of the flour. Knead the dough until it mostly comes away from the sides but still partly remains on the bottom of the bowl, looks smooth, and feels tacky but not too sticky, 15 to 20 minutes (you may need to knead longer depending on your mixer–don't stop until you've successfully completed step 3). NOTE: If it still looks too wet, add the remaining 1 to 2 tablespoons; this will depend on the humidity level in your kitchen and time of year).
3. Grab a small piece of dough and stretch it between your hands to perform a window pane test. If you can stretch it wide and thin enough where light comes through, it’s ready to proof. If it breaks quickly or easily, keep kneading. It’s crucial that you knead the dough long enough in order to get a really feathery, soft texture with lots of gluten development.
4. Cover tightly with plastic wrap (this helps prevent the top from drying out and forming a skin) and place it in a warm spot to rise until doubled in size, about 1 hours. You can check to see if it’s done rising by poking it; if it pops back quickly it needs to rise more, if it comes back slowly or stays mostly dented it’s done.
5. Shape the dough: Divide the dough into 9 equal sized pieces (my risen dough weighed 666 grams so I divided each into balls weighing 74 grams, but if you don’t have a scale just eyeball). Without flouring the surface, use a rolling pin to roll a ball of dough into an 8x3-inch rectangle. Fold it in thirds lengthwise, then turn 90 degrees and use a rolling pin to flatten it again. Roll up into a cylinder, then flip the ends down so it turns into a ball. Cup your hands over and drag it gently across the counter until it’s round and has a smooth surface. Assemble in a 10-inch cast iron skillet lined with parchment paper. Cover tightly with plastic wrap and set aside to proof until nearly doubled in size, another 45 minutes.
6. Bake the buns: While the buns are proofing, preheat the oven to 350ºF with a rack placed in the lower rack. Brush the tops with milk, then bake until deep golden brown and read at least 190ºF on a kitchen thermometer, 30 to 35 minutes (place tin foil on top if browning too quickly).
7. Combine the melted butter and maple syrup; season with a pinch of salt. Brush over the warm buns and sprinkle with a generous amount of flakey sea salt.