Preheat the oven to 400°F.
Slice the tops off the bell peppers (reserve the tops) and scrape out the membranes and seeds. Place peppers standing upright in a baking dish.
In a large saucepan, heat the olive oil over medium heat. Add the onion, carrots, and garlic. Cook, stirring often, until very tender, 8 to 10 minutes.
Add in the rice, thyme, salt, oregano, and black pepper. Stir until the rice is shiny and everything is evenly combined.
Pour the vegetable broth over the vegetables and rice. Bring to a simmer. Cover the pot with a lid and reduce the temperature to a low-medium. Simmer, covered, until all of the broth has been absorbed, 15 to 17 minutes.
Fill the bell peppers with the rice. Add the tops, pressing them gently into the rice mixture.
Add ⅓ cup of water to the dish beneath the peppers.
Cover the peppers tightly with foil. Bake the peppers, covered, for 45 minutes. Then remove the foil and continue cooking, uncovered, for 20 minutes more. Serve with cashew cream.