Preheat the oven to 400°F and line a baking sheet with parchment paper. Divide the pizza dough into 12 equal pieces and roll each into a rope before tying into a simple knot. Place the knots on the prepared sheet.
Bake the knots for 12 to 15 minutes until golden brown. While they bake, stir together the melted butter, 4 minced garlic cloves, olive oil, half the parsley, and salt in a large bowl.
Remove the knots from the oven and immediately toss them in the garlic butter mixture until evenly coated. Sprinkle with black pepper.
In a small saucepan, combine the red wine, balsamic vinegar, sugar, and remaining minced garlic clove. Bring to a simmer over medium heat and cook for 8 to 10 minutes, stirring occasionally, until the liquid reduces by half and thickens slightly.
Transfer the reduction to a small bowl and serve alongside the warm garlic knots for dipping.