Pulse cauliflower in food processor in batches until chopped into ⅛- to ¼-inch pieces, 6 to 8 pulses, scraping down sides of bowl as needed.
Heat 2 tablespoons oil in large saucepan over medium-low heat until shimmering. Add shallot and cook until softened, about 2 minutes. Stir in cauliflower, broth, and salt. Cover and cook, stirring occasionally, until cauliflower is tender, 12 to 15 minutes.
Uncover and continue to cook, stirring occasionally, until cauliflower rice is almost completely dry, about 3 minutes. Stir in remaining 3 tablespoons oil and parsley and season with salt and pepper to taste. Serve.