Slice the leeks in halve lengthwise, and then slice into ¼-inch wide half-rounds. Rinse well in a colander under cold water; drain.

Heat olive oil in a large pot or Dutch oven over medium heat. Add the leeks and cook, stirring often, until they begin to soften, about 3 minutes.

Meanwhile, rinse cauliflower, core, and chop into 1-inch pieces. (This is most easily done by first cutting the cauliflower in half, and then into fourths. Slice out the core, and cut the florets apart.)

Add the garlic to the pot with the leeks and cook, stirring, for 1 minute. Add the cauliflower; cook for 2 minutes to lightly brown.

Pour the vegetable broth into the pot. Increase the heat and bring to a boil. Reduce heat to a low simmer, cover, and cook for about 15 minutes, until cauliflower is tender when pierced with a fork.

Puree soup using an immersion blender or regular blender. If transferring to a regular blender, do so in batches. Do not fill the blender more than half full each time. Return the soup to the pot after blending.

Once soup is pureed, stir in half n half (or milk), and season to taste with salt and pepper. Serve garnished with fresh thyme and/or cheddar cheese, if desired.