Scrub potatoes and cut them into 1/4-inch slices.
Rinse tomatoes, core, and cut each into 6 wedges.
In a 12- to 14-inch frying pan, combine potatoes, tomatoes, lentils, broth, and curry powder. Bring to a boil over high heat, stirring occasionally.
Cover pan, reduce heat, and simmer until most of the liquid is absorbed and potatoes are tender to bite, about 20 minutes, stirring occasionally.
Spoon into wide bowls. Sprinkle with chopped mint and add yogurt and salt to taste.