In a large bowl, combine warm water (110°F), sugar, and active dry yeast. Stir gently and let sit 5-10 minutes until frothy.
Add olive oil and salt to the yeast mixture. Gradually add flour, mixing until a shaggy dough forms. Knead on a lightly floured surface for 10-12 minutes until smooth and elastic (or 8-10 minutes with a stand mixer).
Lightly grease a bowl, place dough in it, turning to coat. Cover and let rise in a warm, draft-free spot for 1 to 1.5 hours, or until doubled in size.
While dough rises, combine minced garlic, dried/fresh mixed herbs, grated Parmesan cheese, red pepper flakes, and shredded mozzarella in a small bowl. Set aside.
Punch down risen dough and roll it into a 12×18 inch rectangle on a lightly floured surface. Evenly spread the garlic herb mixture over the dough, leaving a ½ inch border on one long edge.
Roll the dough tightly into a log from the long edge without the border, pinching the seam to seal. Slice the log lengthwise down the middle. Twist the two halves together, keeping the cut sides exposed. Pinch ends to seal.
Carefully transfer the braided dough to a parchment-lined baking sheet. Cover loosely and let rise again for 30-45 minutes in a warm spot, until visibly puffy.
Preheat oven to 375°F (190°C). Whisk 1 tbsp melted butter and brush over the dough. Bake for 25-35 minutes, or until deeply golden brown and hollow when tapped (internal temp 200-210°F). Tent with foil if browning too fast.
Transfer bread to a wire rack and cool for at least 15-20 minutes before slicing with a serrated knife. Garnish with fresh parsley. Serve warm and enjoy!
Store leftovers in an airtight container at room temperature for 2-3 days, or freeze for up to 1 month. Reheat gently in the oven.