In a large pot or Dutch oven, heat olive oil over medium heat. Add the sliced leeks and cook for 3 to 4 minutes, stirring occasionally. You want them just glistening here, without any browning.

Add in your potatoes and season with salt and pepper. Toss to combine with your leeks. Add your broth and bring this to a boil, then reduce to a gentle simmer and cover the pot.

Cook your potatoes for 15 to 20 minutes until they are just about fork-tender. 4 to 5 minutes before your potatoes are done, add in your broccoli and continue simmering uncovered for another 4 to 5 minutes until the broccoli and stems are blanched, turned a vibrant green, and are fork tender.

Transfer to a blender, or use an immersion blender to completely blend your potato, leek, and broccoli mixture.

Transfer back to the pot on low heat. Add in heavy cream, vinegar, sugar, salt, and pepper to taste. Stir to combine.

To serve, ladle into bowls, topping with fresh chives, a drizzle of olive oil and cream, and a big crack of black pepper.