1. In a large mixing bowl, combine the warm water, sugar, and yeast. Let it sit for about 5 minutes until it becomes frothy.
2. Add the flour and salt to the yeast mixture. Mix until a soft dough forms, then turn it onto a floured surface and knead for about 8-10 minutes until smooth and elastic.
3. Place the dough in a lightly oiled bowl, cover it with a damp cloth, and let it rise in a warm place for about 30 minutes or until doubled in size.
4. Preheat your oven to 375°F. Line a baking sheet with parchment paper.
5. In a small bowl, mix the melted butter, olive oil, parsley, rosemary, thyme, and garlic. Set aside.
6. Once the dough has risen, roll it out into a rectangle approximately 12×18 inches on a floured surface.
7. Brush the herb and garlic mixture evenly over the dough, then sprinkle with Parmesan cheese.
8. Starting from one long side, roll the dough into a tight log. Cut into 12 equal pieces and place them cut-side up on the prepared baking sheet.
9. Brush the tops with beaten egg to give them a beautiful golden color once baked.
10. Bake for 20-25 minutes or until the rolls are golden brown and cooked through.
11. Let them cool slightly before serving warm.

Remember, the key to a perfect swirl is a tight roll and even slices. And don’t worry if they’re not all the same size — that rustic look is part of their charm!