Add 80 grams whole milk and 16 grams bread flour to a small saucepan and whisk until mostly smooth (it's okay to have a few, small lumps -- these will smooth out when you heat the mixture). Set the saucepan on medium heat. Whisk constantly as the mixture begins to thicken into a paste with the consistency of mashed potatoes, about 2 minutes (when done, a thermometer inserted into the paste should reach 149°F). Remove from the heat, then cool to room temperature.
For the dough:
Meanwhile, activate the yeast.Heat 100 grams whole milk in a heat-safe measuring cup for 15 to 20 seconds until lukewarm, but not hot (if the mixture feels hot, let cool to prevent killing the yeast). Stir in 5.4 grams active dry yeast, and let proof for 5 minutes until liquid foams and bubbles.
In the bowl of a stand mixer, add the 314 grams bread flour, 1 large egg, 6 grams Diamond Crystal Kosher Salt, 16 grams granulated white sugar, and 42 grams unsalted butter, cut in ½-inch pieces. Use a spatula to scrape in the tangzhong and yeast-milk mixture. Using the dough hook, knead on low speed for 1 to 2 minutes until a shaggy dough forms.
Increase the stand mixer to medium speed and knead for 8 to 10 minutes. At this point, the dough should be soft and smooth, and slightly tacky but not sticky. Use your hands to form the dough into a ball, then remove from the stand mixer and set aside temporarily.
Wipe the stand mixer bowl, removing any dry bits of flour. Grease the bowl with a bit of oil, then place the dough back inside the bowl and cover with plastic wrap or a damp towel. Let rise at room temperature for about 90 minutes to 2 hours until the dough has doubled in volume.
Grease an 8-inch square baking pan all over with oil, then line the bottom with parchment to prevent any sticking.
To shape the rolls, punch down the dough to expel any air, then roll out into a 10-inch by 14-inch rectangle with a rolling pin.
Sprinkle the dough evenly with 147 grams grated cheddar cheese and 72 grams drained and finely chopped pickled jalapenos, leaving a ½-inch rim around the edges.
Carefully and tightly begin rolling up the end of the dough facing you. Continue rolling until the dough into a log shape and pinch to seal the ends.
Use a sharp knife to cut the dough into 9 equal portions. When cutting the dough, make sure to use a sawing motion and gently move the knife back and forth as you cut down (this prevents the filling from being "squeezed" and spilling out).
Evenly place each bun inside the baking pan and cover with plastic wrap. Let rise for 45 minutes to an hour, or until a finger, gently pressed into the dough, slowly springs back.
15 minutes before the dough finishes rising, preheat the oven to 350°F. Beat the egg.
With a pastry brush, lightly brush the tops of the rolls with 1 large egg and sprinkle with Flaky salt.
Bake the rolls in the oven for about 25 to 30 minutes and rotate the pan halfway through. The rolls are finished when the tops are nicely golden-brown.
Remove the rolls from the oven and immediately brush with 2 tablespoons butter, melted. Let cool in the pan for 10 minutes, then transfer to a wire rack and cool completely (or, let's be honest, dig in if you want to eat them warm!)
Notes
Don't skip the Tangzhong: The tangzhong method of cooking flour and water (in this case, milk) into a paste really helps bring a moist, fluffy roll.
Try to roll up the log as tightly as possible: A more tightly rolled log will have better structure (and won't fall apart).
Omit the pickled jalapenos if you don't like spice: These buns can easily omit the pickled jalapenos if you just want the cheesy flavor. I do love the combo of spicy, tart jalapenos with cheddar cheese, though!
For best results, use a scale. A scale ensures the most accurate results!