Bring a large pot of salted water to a boil and add the orecchiette. Cook according to package instructions until al dente. Reserve some pasta water before draining. This starchy water helps bind the sauce later.
In the same boiling water, add broccoli florets during the last few minutes of pasta cooking. This softens them while keeping their vibrant color. Drain together with the pasta for convenience.
Heat olive oil in a large skillet over medium heat. Add minced garlic and sauté until fragrant but not browned. Stir in chili flakes for a subtle heat boost.
Add the cooked pasta, broccoli, and peas into the skillet. Toss everything together gently. Pour in some reserved pasta water to create a light, silky coating.
Sprinkle freshly grated parmesan cheese over the mixture. Stir until melted and creamy. Season with salt and black pepper according to taste.
Give everything a final toss to combine flavors evenly. Let it cook for another minute so the sauce thickens slightly. Serve warm for the best taste and texture.