Caramelize the onions

• Heat the olive oil and butter in a frying pan over medium heat.
• Add the sliced onions with a pinch of salt and cook slowly, stirring often, until deep golden and soft.

Add the garlic and deglaze

• Stir in the minced garlic and cook until fragrant.
• Add the brown sugar and balsamic vinegar, then pour in the vegetable stock and let it reduce slightly.

Cook the pasta

• Boil the pasta in salted water until al dente.
• Drain, keeping a little of the cooking water.

Combine and serve

• Toss the pasta into the onion sauce, loosening with a splash of cooking water.
• Season with black pepper and finish with grated parmesan.