Preheat oven to 350°F and have an 8"x8" baking dish ready.
Cook the pasta JUST TO AL DENTE, according to package directions. When the pasta has about 2 minutes left to cook, add the broccoli to the still-cooking pasta. Drain the pasta and broccoli and set it aside.
Set a large pot or skillet over medium heat. Melt the butter in the pot, then add the onions. Saute until tender, about 5 minutes. Add the flour, thyme, dry mustard, and smoked paprika and cook, stirring continuously for 3 minutes. Add the garlic and cook for another 30 seconds.
Slowly pour in the vegetable broth, whisking continuously. Add the milk. Increase the heat to medium-high and cook, stirring constantly, until thickened.
Stir in the cooked pasta and broccoli, the drained can of chickpeas, and 2 cups of the cheese. Taste and add more salt and pepper if desired.
Pour the mixture into your baking dish and top with the remaining 1 cup of cheddar, spreading it evenly over the top.
Bake until bubbly and the cheese is melted, 20-25 minutes. Serve.
Notes
Storage/reheating notes:Cover tightly or transfer to an airtight container and store in the fridge for up to 3 days. Warm leftovers in the microwave or gently over the stovetop (you can add a splash of water or broth if needed).