Pour oil into a 12-inch frying pan with 2-inch-high sides (or just an enormous pot if you're as messy as I am) over medium heat. When hot, add garlic and stir until fragrant but not brown, about 1 minute. Add cauliflower and stir to coat, about 1 minute.
Stir in pasta and chicken broth. Bring to a simmer over high heat, then cover, reduce heat, and cook, stirring often, until pasta is just tender to bite and liquid has reduced to a creamy sauce, 15 to 20 minutes. If the mixture begins to stick before the pasta is done, add more chicken broth 1/2 cup at a time. Stir in cheese and salt and chile flakes to taste.