Dice the onion and carrots. Slice zucchinis in half; use a spoon to scoop out seeds, and dice. Slice tomatoes in half; use a finger to scoop out seeds, and dice. Remove stems from kale and dice. Coarsely chop the chicken.
Heat the olive oil over medium heat in a 4-quart saucepan.
Add the onion, carrots, and sea salt; cook for about 5 minutes or until the veggies begin to soften. Add the zucchini, chicken broth, thyme sprigs, and bay leaf. Simmer gently for about 10-15 minutes until the squash is soft. Add the kale.
When kale is bright green (a minute or two), add the tomatoes and chicken. Adjust the seasoning with salt and pepper. Do not overcook the soup or the green vegetables will lose their bright color.
Ladle the soup into bowls and swirl a spoonful of the basil paste atop the soup
