In a large pot, heat the oil over medium heat.
Add the garlic, onion, fennel seeds, bay leaf, and broccoli stems and sauté for 3 to 4 minutes, until the onion becomes translucent.
Add the florets, salt, pepper, red pepper flakes, and enough stock or water to cover the vegetables by about 2 inches. Bring to a boil, reduce to a simmer and cook until the stems become tender, 8 to 10 minutes.
Remove from the heat, discard the bay leaf, and puree the soup in batches. Adjust the consistency as desired with stock or water.
For an optional garnish, reserve 1 cup of the florets and toss them with ¼ teaspoon salt, ¼ teaspoon black pepper, a pinch of red pepper flakes, and 1 tablespoon olive oil, then roast in a 400°F oven for 20 minutes, or until tender and crunchy.