In the bowl of a stand mixer, add the warm water, yeast, and sugar and mix to combine. Let sit for about 5 minutes, or until the yeast mixture starts to get bubbly.
Add the oil, egg, and salt to the yeast mixture and mix to combine, then add 2 cups of flour and begin to mix on low speed using the dough hook attachment. The dough will be very sticky.
Continue to add up to ⅔ cup flour more to the dough until it starts to pull away from the edges of the bowl as you mix. Once you have added all of the flour, mix on low speed for about 2 minutes to knead. Turn the mixer off, cover the bowl loosely with a kitchen towel or plastic wrap, and let the dough rise until light and puffy, or about 30 minutes.
Meanwhile, preheat the oven to 350 degrees F and grease two muffin tins with butter or nonstick cooking spray.
Transfer the dough from the bowl onto a lightly floured work surface and divide into 18 equal pieces. Roll each dough piece into an 8" log. Tie the dough into a knot and place into the prepared muffin tin cup, tucking the ends under the knot. Repeat with all of the rolls.
Melt the butter and mix in the garlic salt. Brush the garlic butter over each dough knot, then add about ½ teaspoon of grated parmesan cheese to each.
Cover the garlic knots loosely and rise again in a warm place for 15-30 minutes minutes, or until the rolls double in size.
Bake in your preheated oven for 12-15 minutes, or until golden brown on top and the internal temperature reads 190 degrees F.
Remove from the oven and let cool for 1-2 minutes, then brush the tops with additional melted butter if desired. Enjoy!