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1
For the spice mixture, combine the spices in a spice grinder and grind to a powder.
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2
Set aside.
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3
For the broth, combine the split peas, turmeric, and 6 cups water in a medium saucepan.
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4
Bring to a boil and skim well.
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5
Then turn the heat down and simmer vigorously, partially covered, until the legumes are tender, 35 to 40 minutes.
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6
Stir occasionally to keep the legumes from sticking to the bottom of the pot, and skim as you need to.
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7
Meanwhile, if using tamarind, measure the warm water into a small bowl or measuring cup.
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8
Add the tamarind concentrate and stir to dissolve it.
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9
Rinse the measuring spoon and your fingers in the water to dissolve all of the sticky tamarind.
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10
Set this tamarind water aside.
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11
Coarsely chop 1 1/2 of the tomatoes and put them in a food processor or blender with the garlic and process to a puree; set aside.
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12
When the split peas are cooked, strain them over a 4-cup or larger measuring cup and reserve for another use (see Headnote).
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13
Add water, if necessary, to the cooking broth to make up 4 cups broth and return to the saucepan.
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14
Add the juiced lemon halves and bring the broth to a boil.
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15
Skim the foam that rises to the top.
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16
Then add the tamarind water, if using, the tomato-garlic puree, the spice mixture, the asafetida, if using, green chiles, and salt.
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17
Turn the heat down so that the soup simmers vigorously and cook, partially covered, for 10 minutes.
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18
Chop the remaining 1/2 tomato and add it to the soup.
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19
Cook 3 more minutes.
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20
For the tempering oil, combine the oil and the mustard seeds, if using, in a small frying pan or saucepan over medium-high heat.
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21
Cover (the mustard seeds splatter and pop) and cook until you hear the mustard seeds crackle, 1 to 2 minutes.
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22
Add the chiles and cook uncovered, stirring, until they start to brown.
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23
Then add the curry leaves, if using, and stir.
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24
(Stand back; curry leaves spit as they hit the hot oil.)
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25
Pour immediately into the soup.
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26
Stir in the lemon juice and the cilantro and serve immediately.
