Melt the butter and olive oil together in a 5 to 6 quart Dutch oven over medium heat. Add the sliced carrots, leek, and onions along with 1 teaspoon of kosher salt. Stir to coat the vegetables, then cover and cook for 10 minutes, stirring occasionally, until the vegetables begin to soften. Next, add the minced garlic and continue to cook for another 2 minutes, stirring often to prevent burning.

Add the cut potatoes and the unsalted vegetable broth to the pot with the sautéed vegetables. Stir to combine, cover, and bring the soup to a boil over medium-high heat.

Once the soup comes to a boil, add in the broccoli florets. Reduce the heat to low, cover the pot, and let the soup cook for about 20 minutes, or until all the vegetables are nice and tender.

Working in batches, carefully ladle the vegetables and broth into a high-powered blender. Remove the center plug from the lid, cover with a kitchen towel, and puree until smooth. I find pouring the first batch into a large measuring cup helpful before blending the rest. Alternatively, you can use an immersion blender to puree the soup directly in the pot.

Return the pureed soup to the pot and taste. Adjust the seasoning with more kosher salt and freshly ground black pepper to taste. Serve the soup hot in bowls, garnished with additional black pepper and freshly snipped chives. For a burst of flavor, I like to add extra chives right before serving.