Step 1

Heat oil in large Dutch oven over medium heat until shimmering. Add onion and broccoli stems and cook until vegetables are softened, 5 to 7 minutes. Stir in garlic and cook until fragrant, about 30 seconds. Stir in flour and cook for 1 minute. Stir in wine, scraping up any browned bits, and cook until almost completely evaporated, about 1 minute.

Step 2

Gradually whisk in chicken and vegetable broths, smoothing out any lumps, and bring to a simmer. Stir in broccoli florets and bay leaf, reduce heat to a simmer, and cook until the florets are tender, 7 to 10 minutes.

Step 3

Remove and discard bay leaf. Working in batches, puree soup in blender until smooth, 1 to 2 minutes. Return soup to clean pot.

Step 4

Stir in half-and-half and additional chicken broth as needed to adjust soup’s consistency. Heat soup gently over low heat until hot (do not boil). Season with salt and pepper to taste and serve.