Halve the leeks lengthwise, discard the woody root end, then slice each half into thin slivers. Transfer the leeks to a bowl of cold water and rinse well. Drain and set aside.
Place a large dutch oven or similar heavy-bottomed pot over medium-high heat. Add the olive oil, followed by the bacon. Slowly render the bacon, stirring occasionally until crisp and browned, about 10-12 minutes. Use a slotted spoon to remove the bacon from the pan but leaving the fat. Transfer the crispy bacon to a paper towel-lined plate.
Add the sliced leeks and onion into the pot with the bacon fat, cook, stirring occasionally, over medium heat until soft and translucent, about 10 minutes. Next, add the chopped cauliflower, garlic, a generous pinch of salt and a few turns of freshly cracked black pepper. Cook and stir for 5 minutes or until the garlic is fragrant and softened.
Next, pour in the chicken stock and fresh thyme. Bring the soup to a simmer then reduce the heat to low, cover and simmer for 20-30 minutes just until the cauliflower is tender and falling apart. Turn off the heat, pluck out and discard the thyme stems then pour in the heavy cream.
To puree the soup, place the blade end of an immersion blender into the bottom of the pot and blend until smooth. Alternatively, transfer the soup to a blender, filling it no more than halfway, place the lid on loosely leaving it slightly ajar so steam can escape then blend on the lowest/slowest setting until smooth and creamy. Repeat as needed until all of the soup is puréed. Taste and adjust the seasonings as needed.
To serve, divide the soup between bowls, top with the bacon lardons, minced chives (or scallions) a few turns of freshly cracked black pepper and a drizzle of olive oil. Serve hot!