Simmer split peas in the water for 18 to 22 minutes until tender but not mushy. Drain extremely well and cool.
Grind the peas with cumin, turmeric, and salt into a fine dry meal.
Make and Fill the Dough:
Mix flour and salt. Add oil and enough warm water for a soft dough. Knead 6 minutes, cover, and rest 30 minutes.
Divide dough and filling into 12 portions. Flatten each dough ball, enclose one filling portion, seal, and rest seam-side down for 5 minutes.
Roll and Cook:
On a lightly floured surface, roll each filled ball very thin, about 9 inches across.
Cook on a medium-hot tawa for 45 to 60 seconds per side, brushing very lightly with oil. Stack under a towel and serve with curry, rougaille, and chutney.
Notes
Do not overcook the split peas or the damp filling will tear the dough.
Keep cooked dholl puri covered so the thin breads stay flexible.