Remove as much peel from the garlic as you possibly can by simply rubbing it with your fingers and cut off the very top to expose a small portion of the cloves. Place each head of garlic on a square of aluminum foil, sprinkle a little bit of salt and pepper and close the foil to seal the garlic in.
Cut cauliflower into florets and lay it in a single layer on baking sheet lined with parchment paper.
Place cauliflower and garlic in the oven and roast for 30-35 minutes, until cauliflower is fragrant, tender, and has taken a nice golden coloration. You’ll want to flip the pieces once halfway through cooking.
In a large sauce pan, cook onion over medium heat until fragrant, about 3-4 minutes. Squeeze the heads of garlic to get the cloves out and add that to the pot, along with apples, cauliflower, salt, pepper, nutmeg, cider vinegar and one cup of water. Bring to the boil and simmer for about 10 minutes.
Remove from heat and allow to cool for a few minutes before transferring to the bowl of your food processor.
Process on high speed and while the motor is running, add Greek yogurt by the spoonful and slowly pour in egg whites. You want to pour them slowly and in a continuous stream so the eggs don’t cook.
Transfer the soup back to the stock pot, add one or two cups of water, depending on desired consistency and bring this up in temperature, almost to a simmer. However, it is very important that you do now allow the soup to boil at this point, again, to avoid cooking the eggs.
For a smoother consistency, strain the soup through a fine mesh sieve before returning it to the stockpot.
Serve warm and garnish with balsamic pearls, dices of apple and fresh basil leaves, if desired.