Heat the oil in a large skillet over medium-high heat. Add the broccoli, then onion, and sauté, stirring frequently until the broccoli starts to turn golden brown, 7 to 8 minutes. Reduce the heat to low and add butter, sugar, and garlic. Continue to cook, stirring occasionally, until the veggies are a rich caramel color, about 10 minutes longer.
Add the dried herbs and spices and cook until fragrant, 30 seconds to 1 minute. Add the broth and bring to a simmer over medium-high heat. Reduce the heat to low and simmer, partially covered, until the vegetables are tender, about 10 minutes.
Transfer to a food processor and puree in batches.
Return soup to the skillet (or pour into a pot if the skillet will not hold the milk). Add enough milk to thin the soup to desired consistency, season with salt and pepper to taste, and heat through. Ladle into bowls, sprinkle pine nuts on top (if using), and serve.
Notes
Nutritional information was figured using whole milk and does not include the optional pine nuts.
If preparing this soup as gluten free, just be sure to use a brand of chicken broth that is labeled as GF.