In a large pot, combine lentils, 2 teaspoons salt, turmeric, and 8 cups water. Bring to a boil, then reduce heat to medium-low and add vegetables. Simmer, stirring often, until vegetables are tender and lentils have broken down, about 45 minutes. Season with more salt, if desired.

Meanwhile, in a large skillet, heat cumin seeds in oil over medium-high until sizzling, 1 to 2 minutes. Add shallots and ginger; cook, stirring occasionally, until brown, 3 to 4 minutes. Add tomatoes; season with salt and pepper. Cook, stirring often, until tomatoes just begin to burst, about 2 minutes more. Spoon tomato mixture over lentils and serve, topped with a dollop of yogurt and mint.