In the bowl of a stand mixer, dissolve the yeast and sugar in the warm water. Let stand for 5 minutes to get foamy.
Mix in the butter, salt, and 3 cups of the flour with a dough hook.
Once well combined, add the last cup of flour ¼ cup at a time until the dough forms a ball, pulls away from the sides of the bowl and is only slightly sticky to the touch. YOU MAY NOT NEED THE ENTIRE LAST CUP OF FLOUR.
Knead for 3 minutes at medium speed.
Cover the bowl with a dish towl and allow dough to rise until doubled. About 30-40 minutes.
Spray a baking sheet with non-stick cooking spray.
Gently dump the risen dough out onto a lightly floured surface. Roll out into a rectangular shape.
Lightly sprinkle the rolled out dough with the garlic salt.
Sprinkle with the green onions, then the mozzarella cheese. Roll up the dough jelly roll style.
Slice the rolled up dough into roughly 15 one inch slices using dental floss or a super sharp knife. I highly recommend the dental floss.
Place the roll slices on the prepared baking sheet. Cover the rolls and let rise for 20-25 minutes. They should nearly double in size.
Preheat the oven to 375 degrees. Bake the mozzarella green onion rolls for 20-23 minutes. The rolls should be slightly browned.