In a medium Dutch oven, bring 2 cups of water to a boil. With the flat side of your knife, crush the head of garlic so the cloves separate from the base. Discard any loose skins. Add the cloves to the boiling water, and blanch for 2 minutes. Using a slotted spoon or a fork, remove the garlic cloves and any wayward skins from the pot, and let them rest on a cutting board until cool enough to handle. Pick the skins off with your fingers—they will come off extremely easily.

Add the garlic cloves back to the pot, along with the chicken stock, quinoa, fennel, salt, and cayenne. Bring to a boil. Cover, and simmer over medium-low heat for 15 minutes, or until the quinoa is cooked. Remove the pot from the heat.

In a shallow bowl, beat the eggs.

Temper the egg: slowly whisk 1⁄4 cup of the hot broth into the bowl, adding a very small amount at a time so as not to scramble the egg. Repeat with another 3/4 cup of broth. Once the egg mixture is warm and the broth is fully incorporated, stir the mixture into the soup and add the lemon juice, shredded chicken and fennel fronds. The egg yolk will give the soup a subtle, silky quality, while the lemon adds brightness to the rich, sweet garlic.

Serve immediately.