In a large pot or rondeau, over medium heat, add the olive oil and sauté the onions and leeks, gently seasoned with salt, for 12 to 15 minutes, or until browned.
Add in the celery and broccoli and sauté for an additional 3 to 4 minutes.
Stir in the garlic and cook just until it becomes fragrant.
Deglaze with the optional wine and cook until only a tablespoon or two remain.
Next, add in the butter and flour, and mix the vegetables around until coated.
Pour in the chicken stock, season with salt, and cook over medium-to-medium-high heat until the broccoli is just tender, about 12 to 15 minutes. The liquid should be thick at this point.
Using an immersion blender, puree the soup until smooth and thick. Alternatively, blend it in batches in a blender, then return it to the pan. Be sure to remove the center cap from the lid and cover with a towel so that the steam can escape.
Finish by stirring in the half-and-half. Adjust any seasonings with salt and ground white pepper.
Serve with optional croutons.
Notes
Another great thing about this soup is that the final consistency is up to you. I prefer my creamy soups super smooth, so I let the immersion blender work its magic for a while. If you want more texture, either blend briefly to leave some small broccoli pieces or stir in a handful of steamed florets at the end.Frozen broccoli: While fresh is my go-to, you can use frozen broccoli if that's what you have on hand.No immersion blender? You can blend batches of the soup in a regular blender instead. Be careful when blending hot liquids; use a venting lid if you have one. You’ll want that steam to escape to prevent splatter or pressure from building up.Temper the dairy: Cold cream will easily curdle in the soup, so to avoid this, I’ll take the half-and-half out of the fridge 20 minutes before pouring it into the pot. Add cheese: When I’m lucky enough to have a leftover Parmesan rind in the fridge, I’ll toss it into the pot when I add the stock and fish it out at the end. Make-Ahead: This is a great make-ahead recipe because the broccoli flavors get even better after sitting. Make it up to 1 day in advance, keep it in the fridge, and then reheat it on the stove the next day.How to Store: Pour the cooled soup into an airtight container and refrigerate it for 3 to 4 days or freeze it for 3 months. Let the leftovers thaw in the fridge overnight, then reheat.How to Reheat: Add as much soup as you plan on eating to a saucepan and warm the leftovers over medium-low heat. You can add a splash of stock if it thickens and needs thinning.