Preheat oven to 450°.
Bring broth (or salted water) up to a boil in a saucepan. Add lentils, cover, and reduce heat to a simmer for at least 25-30 minutes, until tender. Drain any excess liquid.
While lentils cook, toss eggplant and red onion with oil, 1/2 tsp. of the salt, cumin, and garlic powder on a rimmed baking sheet. Roast at 450°, tossing halfway through, until eggplants are charred in spots and tender, 20–25 minutes.
Combine yogurt, tahini, lemon juice, cardamom, and remaining 1/4 tsp. salt in a bowl; whisk in up to 3 tsp. water until desired consistency is achieved.
Prepare bowls by dividing lentils evenly into each of four bowls. Scatter roasted eggplant and red onion overtop. Drizzle with cardamom yogurt and garnish with fresh mint and sliced cucumber, if desired.