Heat the olive oil in a large pot over medium heat. Add the onion, carrots, and celery. Cook for 5 minutes until the vegetables start to soften.
Stir in the garlic and cook for 1 minute until fragrant.
Add the pearl barley and green lentils to the pot. Pour in the vegetable broth, then add the thyme and bay leaves.
Bring the mixture to a boil, then reduce the heat to low. Cover and simmer for 30 minutes, stirring occasionally.
Stir in the white beans and chopped kale. Continue to simmer uncovered for 10 more minutes until the kale wilts and the barley is tender.
Remove the bay leaves. Season with salt and black pepper to taste before serving.