Heat olive oil in a large pan over medium-high heat.
Add diced onion and minced garlic to the pan and sauté for 3-4 minutes until fragrant. Season with a pinch of salt and pepper.
Add dry pasta, yogurt, broccoli, broth, red pepper flakes, and a little more olive oil to the pan. Stir well to prevent sticking.
Cover the pot and reduce heat to medium-low. Let the pasta cook until the liquid is absorbed and noodles are al dente, about 11 minutes (but cooking time may vary).
Once pasta is cooked, remove the cover and stir in 3/4 cup of shredded Parmigiano Reggiano cheese until fully combined.
Serve the pasta topped with remaining cheese. Enjoy! Any leftovers can be stored in the fridge for up to one week in an airtight container.