In the bowl of a stand mixer add yeast (7g) and warm milk (208g). If using active (not instant) yeast, add a pinch of the sugar and let rest 10-15 minutes until bubbly. If using instant (not active) yeast, continue to the next step.
Add the egg (1), gochujang (2 tablespoons), butter (28g), and garlic (1 teaspoon) and mix in with a fork.
Add the bread flour (420g), the sugar (30g), and the salt (7g).
With the dough hook run the mixer on low until incorporated and then increase to medium and let knead for 6-8 minutes. You may need to add another tablespoon of water or flour if the consistency isn't right.
Put into an oiled bowl and cover and let rise for 1-2 hours until doubled.
Punch down, weigh, and divide into 9 pieces.
Put on oiled quarter-sheet pan and let rise just until touching, 45-60 minutes.
Heat oven to 350℉ / 175℃.
Lightly beat egg (maybe with a little water) and brush the tops of the rolls. Bake for 25-30 minutes until a deep brownish orange.