Place the pasta nests in the center of a large pan. Arrange the cherry tomatoes, red onion, garlic, and spinach around them.
Spoon the tomato mixture over the pasta and drizzle with olive oil. Season with oregano, basil, chili flakes if using, salt, and pepper.
Pour in the cream and vegetable broth until the pasta is mostly submerged. Cover with a lid and bring to a gentle boil over medium heat.
Cook for 11–13 minutes, stirring occasionally, until the pasta is tender and the sauce has thickened into a creamy consistency.
Finish with a generous handful of grated Parmigiano Reggiano, stirring it in just before serving. Garnish with extra cheese on top.
