Make the tamarind-date chutney: Combine seedless tamarind, dates, and water (for tamarind-date chutney) in a small saucepan. Bring to a simmer over medium heat and cook until the tamarind softens and dates are mushy, 10β12 minutes. Stir in jaggery until dissolved, then remove from heat and cool 5 minutes. Blend the mixture until smooth, strain back into the pan, and stir in roasted cumin powder, kashmiri red chili powder, and dry ginger powder. Simmer 3β5 minutes more until glossy and pourable. Cool completely.
Make the green chutney: In a blender, combine cilantro leaves (2 cups), fresh mint leaves, green chilies (2), ginger, lemon juice, sea salt, sugar, and water (for green chutney). Blend until very smooth, adding a splash more water only if needed. Set aside.
Cook the potatoes: Bring water (for boiling potatoes) to a boil in a pot. Add potatoes and simmer until just tender when pierced, 18β22 minutes. Drain, cool until handleable, peel, and dice small.
Refresh the puffed rice: In a wide skillet over medium heat, dry-roast puffed rice (murmura), stirring, until crisp and warm, 2β3 minutes. Spread on a tray to cool completely.
Assemble the bhel: In a large mixing bowl, combine diced potatoes, red onion, tomato, green chili, roasted peanuts, and chopped cilantro leaves (0.5 cup). Add fresh lime juice, chaat masala, and black salt; toss to coat evenly. Add green chutney (6 tbsp) and tamarind-date chutney (6 tbsp) and toss again until everything is lightly coated.
Finish and serve: Add papdi and the cooled puffed rice to the bowl and toss quickly just to combine, 10β15 seconds. Fold in nylon sev. Divide immediately into 4 bowls and serve at once while everything is crisp.