Step 1

In a Dutch oven or similar large, deep pot, melt the butter over medium heat. Add the leeks. Cook, stirring occasionally, until the leeks are very soft, about 10 minutes. Adjust the heat as needed so the leeks sweat but do not brown.

Step 2

Stir in the garlic, salt, and pepper. Sprinkle the flour over the top. With a wooden spoon, stir vigorously for 1 full minute. All of the white bits of flour should disappear (this makes the soup thick and yummy).

Step 3

Slowly pour in the vegetable broth, stirring constantly and pausing periodically between additions so that lumps do not form.

Step 4

Add the potatoes. Increase the heat to high and bring to a steady simmer, then cover the pot and reduce the heat to low. Let simmer, covered, until the potatoes are super soft and beginning to fall apart, about 25 to 30 minutes.

Step 5

With an immersion blender, puree the soup until thick and smooth, adding milk as needed if it is thicker than you would like; if you don’t have an immersion blender, add a few ladlefuls to a regular blender and carefully puree (be careful! hot soup splatters). Stir the blended soup back into the pot; repeat as needed.

Step 6

Add a few spoonfuls of the hot soup into a medium bowl. Add the Greek yogurt and stir to combine (this helps temper the yogurt to deter curdling).

Step 7

Stir the yogurt mixture back into the soup.

Step 8

Add the vinegar, mustard, and dill. Stir in half of the green onions. Taste and adjust the seasoning as desired. Serve hot with the remaining green onions sprinkled over the top and a few grinds of black pepper.