Set a 4-6 quart saucepot over medium heat. Add the sesame oil, chopped onion, garlic, and ginger. Sauté for 5-7 minutes to soften.
Stir in the tomato paste, salt, cumin, coriander, turmeric, and cardamom. Sauté another minute or two.
Pour in the vegetable broth and split peas. Bring to a boil. Stir and reduce the heat to a simmer. Simmer the daal for 30-40 minutes, until the peas are soft. (Red lentils will take approximately 20-25 minutes.)
Taste, then salt and pepper as needed. Add additional broth if you would like the daal a little thinner.
Serve warm with basmati rice.
