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Place the water in the bowl of a stand mixer. Stir in the yeast & sugar & let sit until foamy, about 10 minutes.
Add the oil, egg, salt, & 2 cups flour. Mix on low speed with the paddle attachment until combined.
Switch to the dough hook & add 1 cup flour. If dough is still wet & sticky, add remaining ½ cup. Knead until the dough is smooth & elastic, about 5 minutes.
Immediately divide the dough into 3 ounce pieces (I got 12 buns). Flatten each piece, then use a rolling pin to roll into a rectangle, roughly 6"x4".
Starting at a long end, roll dough into a log. Pinch the seam, then gently tuck the ends under.
Place on a baking sheet lined with parchment, flattening each slightly with your hand. Cover with a damp towel and set aside for 10 minutes while the oven preheats.
Preheat oven to 425°F. Whisk together the egg yolk & water, then brush over the buns.
Place the buns into the preheated oven. Cook for 9-14 minutes or until the buns are deeply browned & are fully cooked.