Pour 1 tablespoon olive oil in a large pot over medium heat. Add the carrots, celery and onion, then cook, stirring occasionally, until softened, about 5 minutes. Add the garlic and cook for 2 minutes more. 

Add the chicken stock and white beans, stir, then submerge the chicken breasts. Cover, bring to a boil, then reduce the heat and simmer until the chicken is cooked through, about 10 minutes. 

While the chicken cooks, make the pesto. Add 1 large or 2 smaller cloves garlic to the bowl of a food processor. Pulse until coarsely chopped, then add the pine nuts and basil. Continue pulsing as you slowly stream in the olive oil. Add the parmesan cheese and pulse a few more times until everything is well combined. Season to taste with salt and pepper. 

Remove the chicken breasts and let cool, then use two forks to shred into bite sized pieces. Add the chicken back to the pot along with the kale, stir, then cover and cook just a few minutes more until the kale is wilted.

Stir in the pesto and lemon juice, then ladle into bowls. Sprinkle with more grated parmesan and a drizzle of olive oil, then serve it piping hot.