Smoked Mozzarella Mezzelune with Braised Onion Sauce

Name: Smoked Mozzarella Mezzelune with Braised Onion Sauce
Ingredients: 6 tablespoons unsalted butter (3 ounces), divided; 4 medium onions, chopped into 1/2- inch pieces (about 6 cups); ½ teaspoon kosher salt, divided, plus more to taste; 3 large garlic cloves, thinly sliced; ¼ cup tomato paste; ½ cup dry white wine; 3 cups vegetable stock, plus more as needed; 2 bay leaves; Small pinch of ground cloves (optional); 1 teaspoon high-quality balsamic vinegar (optional); ¼ teaspoon black pepper, plus more to taste