Heat coconut oil in a large pot over medium heat. Add onions and sauté until golden (about 5 minutes). Add garlic and stir for another minute.
Add vegetable broth to the pot. Stir until producing a light steam. Add the broccoli florets in with the mixture and let steam for 5 minutes or until broccoli is bright green.
Add salt to taste.
Add coconut milk and stir well.
Add spinach and kale. Stir just until the greens are wilted and remove from heat.
In your food processor or magic bullet, blend the soup until smooth. If you are using a blender, ensure to remove the middle piece of the lid to allow steam to escape.
Transfer blended mixture back into a large pot. Warm to desired temperature.
Ladle into bowls. Drizzle with a splash of olive oil, lemon juice and garnish with avocado slices.