Step 1

Heat butter and oil in a Dutch oven over medium heat until the butter melts. Add onion and celery; cook, stirring occasionally, until softened, 4 to 6 minutes. Add garlic and thyme (or parsley); cook, stirring, until fragrant, about 10 seconds.

Step 2

Stir in broccoli. Add water and broth; bring to a lively simmer over high heat. Reduce heat to maintain a lively simmer and cook until very tender, about 8 minutes.

Step 3

Puree the soup in batches in a blender until smooth. (Use caution when pureeing hot liquids.) Stir in half-and-half (if using), salt and pepper.