Put the kneader attachment onto the stand mixer.
In the stainless steel bowl of a stand mixer, dissolve the yeast with 1 teaspoon sugar and ¾ cup distilled water, at room temperature.
In another bowl whisk together the 3 ½ cups flour, salt, 1 Tablespoon sugar.
Add the dry ingredients on top of the yeast mixture.
Start the mixer on low speed and start to pour about ½ up of the remaining distilled water into the bowl as it is kneading. Save the remaining ¼ cup water in case the dough is too dry.
Add the butter and the olive oil to the dough as the mixer is kneading.
If dough seems too dry, add water 1 Tablespoon at a time.
Total kneading time should take about 8 minutes. when finished kneading the dough, it should feel soft but semi-sticky and smooth. It should only slightly stick to you hands when removing from the bowl.
Do not add too much flour or the buns will be heavy.
Remove the dough to a very lightly floured surface; cover with a clean tea towel (not terrycloth) and let rest 5 minutes.
Shape into a ball (the dough will come together nicely after resting).
Place into a large greased deep container.
Cover and let rise in a warm place for about 60-90 minutes.
To check if the dough is ready to be punched down, very gently stick two fingers about ½-inch into the dough, the dough is ready when the finger marks remain.
Punch down dough and slice in half.
Slice each half into 6 even pieces. (12 total)
Shape each piece into a round ball.
Place balls spacing well apart onto a large oiled parchment lined baking sheet.
Cover and let rise 30-40 minutes.
Right before placing in oven, lightly brush with beaten egg white.
Bake at 375 F. for about 22 minutes or until light golden brown.