In a medium saucepan, bring 2 1/4 cups of water to a boil. Add the rice and 1/4 teaspoon of the salt, reduce to a simmer, cover and cook until the rice is tender about 17 minutes.
Meanwhile, in a large nonstick saucepan, heat the oil. Add the onion and garlic and cook, stirring occasionally, until the onion is softened, about 7 minutes. Add the carrots and cook, stirring occasionally, until the carrots are crisp tender, about 4 minutes.
Add the lentils to the pan, stirring to coat. Add the tomatoes, broth, ginger, coriander, allspice, and the remaining salt and bring to a boil. Reduce to a simmer, cover, and cook until the lentils have begun to soften, about 10 minutes. Stir in the cauliflower, cover, and cook until the lentils and cauliflower are tender, about 10 minutes.
Serve lentils and cauliflower stew over rice with a dollop of yogurt.