First, heat the olive oil in a large heavy soup pot over medium-high heat. Once the oil is shimmering, add the finely chopped onion. Cook it until the onion is softened and starts to brown, stirring occasionally. This process should take about 5 to 7 minutes. The onions will caramelize slightly, adding sweetness to the soup.
Next, add the dried parsley and dried thyme to the pot. Stir these herbs in and let them cook for a minute or two more to release their fragrant oils, blending beautifully with the onion.
Now, pour in the chicken broth. Let the broth simmer gently for about 10 to 15 minutes. This simmering allows the flavors to meld together, creating a delicious foundation for your soup.
Add the cauliflower rice to the pot next. Allow it to simmer over medium-low heat until it is tender or until the cauliflower is fully cooked—this should take around 20 to 25 minutes. If using frozen cauliflower rice, start checking for doneness after about 15 minutes.
Once the cauliflower is cooked, stir in the diced leftover chicken. Turn the heat down to the lowest possible setting and let it cook for about 5 more minutes. This allows the chicken to warm through without getting tough.
While the soup gently simmers, zest a lemon and squeeze additional lemons to get about 1/4 cup fresh lemon juice. The zest will add a lovely brightness, while the juice enhances the soup’s flavor.
Next, beat the eggs in a bowl until they’re frothy, then whisk in the lemon juice and lemon zest. This mixture will create a creamy texture in the finished soup.
Remove a cup of hot broth from the soup and let it cool slightly. This is important to avoid cooking the eggs too quickly. Once cooled, whisk in 1/2 cup broth into the egg mixture, beating well. Repeat with another 1/2 cup.
Finally, whisk this creamy mixture back into the big pot of soup. Ensure the temperature is very low at this point to prevent boiling, as it can curdle the eggs. Let the soup heat gently for a few moments, allowing everything to meld together beautifully. Serve it warm and enjoy!