Bring a large pot of well-salted water to a boil and cook pasta according to package directions until al dente. Reserve 1 cup of pasta cooking water before draining.

Meanwhile, heat olive oil and butter in a wide skillet over medium-low heat. Add sliced onions and a pinch of salt. Cook slowly, stirring occasionally, until onions are deep golden and caramelized, about 25–30 minutes. Lower heat if onions brown too quickly.

Stir in garlic and thyme, cooking 1–2 minutes until fragrant.

If using cream, pour it in now and bring to a gentle simmer, stirring to incorporate the caramelized onions. Let cook 2–3 minutes until slightly thickened.

Add the cooked pasta to the skillet along with Parmesan. Toss well, adding reserved pasta water a little at a time until sauce reaches desired consistency.

Season generously with salt and plenty of black pepper. Taste and adjust.

Serve immediately, topped with more Parmesan and a sprinkle of chopped parsley if desired.