Melt the butter with olive oil in a large skillet over medium heat. Add onions and ¼ teaspoon salt. Cook for 10 minutes, stirring often, until softened.

Lower heat to medium-low. Continue cooking for 25–40 minutes until the onions are deeply golden and soft. Stir frequently; add a tablespoon of water if browned bits start to scorch.

Meanwhile, bring a large pot of water to a boil. Salt lightly and cook the rigatoni according to the package timing, stopping when just al dente. Reserve 1 cup of cooking water, then drain.

Stir garlic, thyme and pepper into the onions for 1 minute. Add the broth and scrape the pan gently. Simmer for 3–5 minutes, until slightly reduced.

Add the drained pasta and ¼ cup reserved cooking water to the skillet; toss over low heat for 1 minute. Remove from the heat and stir in Gruyere in small handfuls. Add more reserved water a splash at a time until the sauce coats the pasta loosely. Taste and serve immediately.

Refrigerate leftovers promptly in shallow containers. Use within 3–4 days and reheat throughout to 165°F (74°C), adding a splash of water as needed.