Braised Radicchio and Caramelized Onion Pasta - SippitySup

Ingredients

• 3 tablespoons unsalted butter divided
• 2 tablespoons olive oil divided
• 1 teaspoon fresh thyme leaves
• ½ teaspoon kosher salt plus more for seasoning and pasta water. as needed
• 4 medium onions peeled and thinly sliced
• 2 teaspoons red wine vinegar divided
• 2 tablespoons water divided
• freshly ground black pepper as need, to taste
• 2 cloves garlic peeled and minced
• 1 medium radicchio quartered lengthwise
• vegetable stock as needed
• 1 teaspoon granulated sugar
• 1 pinch crushed red pepper flakes or to taste
• 1 pound dried pasta
• ¼ cup grated Parmesan cheese plus more as needed