Preheat oven to 400 degrees F.
Place broccoli and chickpeas on a baking sheet.
Roast in oven until broccoli starts browning.
Meanwhile, cook pasta al dente, according to instructions on package.
Rinse with cold water to stop cooking.
Drain and set aside.
Whisk together remaining ingredients, except shallots, in a small bowl.
Heat large skillet over medium heat.
Saute shallots until slightly browned.
Use a small amount of broth or water to prevent sticking, if necessary.
Add broccoli, chickpeas, pasta, and sauce to the skillet, stirring constantly, until the sauce has thickened.
Add additional broth if you want a creamier dish.