Remove the leaves and the core of the cauliflower. Slice up the softer parts of the core to use in the soup. Slice the cauliflower into ½ inch slices. Keep out about a cup of small cauliflower florets to brown and use as a garnish.
Cut up a leek, using the white and light green parts. Slice this into thin slivers along the length and wash if necessary.
Halve the onion and thinly slice.
In a heavy sauce pan or dutch over, melt 3 tablespoons of butter, then add the leeks, onion and 1 ½ teaspoons of salt. Keep the heat on medium low and soften for about 10 minutes without browning.
Raise the temperature to medium high and add 4 ½ cups of water and half of the cauliflower and the core pieces. Bring to a boil and simmer for 15 minutes.
Add the remainder of the cauliflower and simmer for an additional 20 minutes.
While the soup is boiling, melt 5 tablespoons of butter in a small skillet and add the reserved florets. Keep the heat on medium and stir frequently to brown the cauliflower. This will take 7 or 8 minutes. Remove the florets with a slotted spoon stir in vinegar and save for garnish, along with the browned butter.
Remove soup from the heat and use an immersion blender to puree. This will take several minutes. You can also use a countertop blender for this but make sure that you take the stopper out of the blender cover and use a towel to cover the opening. This will let the steam escape and not overflow. Start slowly by pulsing a few times. The hot liquid steams and expands while being blended. Just be careful. You may want to do this in two batches. Blend until smooth which should take about 50 or 60 seconds.
Rinse the sauce pan or dutch oven and return the soup. On medium heat, bring to a simmer and then thin the soup with water until the surface remains flat after stirring. Add 1/4 cup at a time until thinned.
Garnish with browned florets, browned butter, chopped chives and black pepper.