Peel and halve the yellow onions, then slice them into very thin, even half moons on a stable cutting board.

Melt butter with olive oil in the Dutch oven over medium-low heat. Add onions and salt. Cook for 35–45 minutes, stirring regularly, until deeply golden and very soft. Add small splashes from the measured water if the onions threaten to scorch, and lower heat if needed. Extend cooking if the onions are still pale.

Stir garlic, thyme, and black pepper into the onions for 1 minute. Pour in beef broth and scrape up the browned bits. Bring to a gentle boil.

Stir in dry rigatoni and simmer uncovered over medium-low heat, stirring often, for about 12–15 minutes or until tender with a slight bite. Check the pasta package and begin tasting near its suggested time. Add remaining measured water gradually if the pan becomes dry before the pasta is tender; use extra small splashes only if necessary. Reduce excess liquid briefly if needed, keeping a loose sauce.

Stir in heavy cream and warm for about 1 minute. Remove from the heat and stir in most of the Parmesan, reserving a little for the bowls. Cover and rest for 5 minutes. Loosen with a splash of hot water if needed, divide into 4 bowls, and finish with parsley and reserved Parmesan.