Heat the oil in a large saucepan, cast iron pan, or dutch oven medium heat. Add the onions and carrots and cook for about 10 minutes.
Add the garlic, and stir for a minute or two until fragrant.
Add the eggplant, lentils, tomatoes, and the rest of the seasonings.
Bring to a boil, then cover and reduce heat to a simmer. Simmer until the lentils are fully cooked, stirring occasionally and adding broth or water as needed.
The time will vary depending on the type and freshness of your lentils. Mine took a little over an hour.
To make this in an Instant Pot, see notes below.