Heat olive oil in a deep-frying pan or wok over medium-high heat. Add garlic and cook, stirring occasionally, until browned, about 1 minute. Remove to a plate; chop and set aside.
Place cabbage into the pan and stir-fry for 1 to 2 minutes; add kale and onions. Stir-fry until kale is bright green and tender, about 5 minutes.
Add chicken broth, carrots, salt, and red pepper flakes. Cover and let steam, 2 to 3 minutes. Remove from heat, add chopped garlic, and serve.
