To a large pot on the stove and over high heat, add the wild rice, butter, vegetable broth, and seasonings. Stir well. Bring to a simmer, then turn the heat to low and cover with the lid. Let simmer for 40 minutes.
Once time is up, stir in the minced garlic, then add in the remaining ingredients. Stir well and cover with the lid. Let cook for 5-10 minutes or until the broccoli is tender.