Combine all the spice mix ingredients in a small bowl and set aside.
Heat oil in a large pot over medium heat. Add carrots, onion, and garlic. Cook, stirring often, until softened, about 2-3 minutes. Reduce heat if the garlic starts to brown.
Stir in about a half-cup (118 mL) of water and the spice mix. Reduce heat to low and simmer for about 3-4 minutes.
Stir in salt, tamari, remaining water, and lentils. Bring to a boil over high heat, then reduce heat, cover, and simmer for about 45 minutes to 1 hour, stirring occasionally. Lentils should be soft but not mushy. Cook longer if needed. If soup is too thin near the end of cooking time, remove the lid and turn up the heat to gently boil off some of the liquid. See Notes.
Stir in tomato paste and, if needed, add enough vegetable stock to get to the consistency you like. Taste and add a pinch more salt, if necessary.
Serve alongside crusty bread and a salad of bitter greens or a basic garden salad, if you prefer.