Special equipment: a deep-fry thermometer; a Parisian scoop or small melon baller
Place the cauliflower florets in a large pot with the onion, thyme sprigs and milk. Slowly bring to a boil over medium-high heat. Season with kosher salt, cover and simmer until the cauliflower is soft, 25 to 30 minutes. Discard the thyme sprigs. Transfer the cauliflower mixture to a blender and puree until completely smooth. Taste and season with salt.
Fill a medium saucepan with 2 to 3 inches of olive oil and heat to 350 degrees F. Fry the Brussels sprout leaves a few at a time until browned, 30 to 40 seconds. Drain on paper towels and season with fleur de sel.
To serve, scoop the apple into balls with a Parisian scoop or small melon baller. Or, just dice the apple if a scoop is unavailable. Ladle the soup into shallow bowls or small shot glasses or espresso cups and garnish with the fried Brussels sprout leaves. Sprinkle with the chives, lemon thyme leaves, apple balls and season with fleur de sel and cracked black pepper. Drizzle with the smoked olive oil.
When blending hot liquid, first let it cool for five minutes or so, then transfer it to a blender, filling only halfway. Put the lid on, leaving one corner open. Cover the lid with a kitchen towel to catch splatters, and pulse until smooth.