In a large pot, heat the butter and olive oil on medium heat, when hot, add the onion, carrot, celery. Cook, stirring often until the onion is tender and translucent.
Add the garlic, thyme, turmeric, red pepper flakes (if using), the 1/4 teaspoon salt, and the bay leaf. Stir together and cook the mixture for 1 minute.
Add the broth and chickpeas, stir to mix, and bring to a boil. Reduce to a simmer then cover let this cook 20 minutes, stir occasionally.
Remove the bay leaf then add the cooked rice and stir into the soup. Taste and adjust seasoning with salt and pepper. Simmer for a few minutes to warm the rice through.
Ladle into bowls and serve.