Step 1: Grease 12 jumbo muffin tins.
Step 2: In a cup or bowl proof the yeast with 1 teaspoon sugar in warm water until foamy (about 10 minutes, if the yeast is not foamy discard and start again).
Step 3: In the stainless steel mixer bowl combine 3 cups flour, 4 tablespoons sugar, melted butter, warm milk, egg and salt, then add in the yeast mixture
Step 4: With a kneader blade fitted on a heavy-duty mixer start kneading adding in more flour or water if needed to create a soft semi-sticky smooth dough (do not add in too much flour or the baked buns will have a heavy texture (IMPORTANT! stop the kneading after about 5-7 minutes and allow the dough to rest for 15 minutes, then finish the kneading process).
Step 5: Remove from the bowl and let rest on the counter covered with a clean tea towel for 10 minutes.
Step 6: After 10 minutes shape into a ball (the dough will come together nicely).
Step 7: Coat a glass or stainless steel bowl with oil, then place the dough in and turn to coat.
Step 8: Cover and allow to rise until doubled (because of the addition of egg the dough will take longer to rise, rising time may take about 1-1/2 hours).
Step 9: Punch down the dough, then remove from bowl then place the dough on the counter.
Step 10: Slice the dough evenly in half lengthwise down the middle, then shape each piece of dough into a chunky long rope using hands.
Step 11: Slice each rope into 18 even pieces (don’t worry if each piece of dough is not the exact same size).
Step 12: Shape into about 1-1/2-inch balls or a little more, then place 3 balls into each muffin tin.
Step 13: Repeat with remaining “rope”
Step 14: Cover the tins with a clean dry tea towel and allow to rise warm place for 30-40 minutes (rising time will depend on the temperature of your kitchen).
Step 15: Brush tops with melted butter, then bake in a preheated 375 degree F oven for about 20-25 minutes or until buns are a dark golden color.
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