Heat the oil over medium heat and cook the carrots and onion 5-10 minutes, stirring.
Add the lentils, rice, salt, cumin, pepper, broth, and tomato sauce. Bring to a boil, stir, cover, reduce heat, and simmer 45 minutes--until the lentils are tender.
Use a hand immersion blender to blend the soup or transfer it half at a time into your food processor or blender and blend a bit. I personally like it to still be a bit chunky so I didn't make it totally smooth.
Stir in the milk and heat over low until warmed through.