STEP 1
In a large saucepan or stockpot, heat olive oil, then add onion, carrot, and celery. Add a pinch or two of salt and a couple grindings of pepper. Cook on medium until softened, then add garlic and sauté a bit longer until fragrant.
STEP 2
Add the vegetable stock, bay leaf, thyme, and potatoes. Season with a few pinches of salt and grindings of pepper. Bring to a boil then reduce heat to simmer.
STEP 3
While the potatoes cook, prepare the kale by washing and removing thick stems. Stack the leaves on top of each other, roll them up into a cigar, and slice crosswise into thin ribbons. Add the kale to the pot. If necessary, add more stock or water to the pot.
STEP 4
Cover and let the soup cook until the potatoes are easily pierced with a fork, and when a ribbon of kale has become tender; about 10 to 20 minutes.
STEP 5
Turn off the heat and stir in the lemon juice. Taste and season with more salt and fresh pepper as needed. To finish, crack the eggs into small cups or ramekins. Gently slide them into the soup. Ladle some of the broth on top of the eggs to submerge them. Put the lid back on the pot and let sit for about 4 minutes or until the whites of the eggs are opaque and the yolk is still soft. If the eggs break into the soup before they are poached, use a fork to swirl them into the soup, like egg drop soup.
STEP 6
Ladle the soup into serving bowls, then carefully spoon all or part of the eggs on top. Finish with a grated Parmesan cheese and a drizzle of good olive oil.