Step 1

Toast ½ cup unsweetened shredded coconut in a dry medium skillet over medium heat, stirring often, until golden brown, about 4 minutes. Transfer to a food processor and let cool.

Step 2

Add 4 garlic cloves, unpeeled, smashed, to same skillet and cook, turning occasionally, until golden and fragrant, about 2 minutes. Transfer (skin and all) to food processor along with 2 tsp. Kashmiri chile powder or paprika, 1 tsp. Diamond Crystal or ½ tsp. Morton kosher salt, and ½ tsp. cayenne pepper. Pulse until mixture is coarsely chopped (small pieces of garlic peel are okay).Do Ahead: Chutney can be made 2 days ahead. Transfer to an airtight container; cover and chill.

Step 3

Whisk 1 cup chickpea flour, 2 Tbsp. rice flour, 1½ tsp. Diamond Crystal or 1 tsp. Morton kosher salt, ½ tsp. ground turmeric, ⅛ tsp. cayenne pepper, and ¾ cup water in a medium bowl until smooth. Set batter aside.

Step 4

Place 2 lb. medium russet potatoes, peeled, in a large pot and pour in water to cover by 2"; season generously with salt. Bring to boil and cook until potatoes are fork-tender, 25–30 minutes. Drain potatoes and return to pot (off heat); let cool slightly. Using a fork, coarsely mash potatoes; set aside.

Step 5

Heat 1 Tbsp. plus 1½ tsp. vegetable oil in a medium pot over medium-high until shimmering. Cook 10 fresh curry leaves, one 2" piece ginger, peeled, finely chopped, 2 green Thai chiles, thinly sliced, ⅛ tsp. asafetida, and 1 tsp. black mustard seeds, stirring, until mustard seeds begin to pop and curry leaves are fragrant, about 30 seconds. Stir in remaining ½ tsp. ground turmeric.

Step 6

Scrape curry-leaf mixture into pot with reserved potatoes; mix until potatoes are evenly stained with turmeric. Mix in ½ bunch cilantro, leaves chopped, 2 Tbsp. fresh lime juice, and 2½ tsp. Diamond Crystal or 1½ tsp. Morton kosher salt. Taste and add more salt if needed. When mixture is cool enough to handle, form into six 4"-diameter patties; flatten tops.

Step 7

Pour vegetable oil into a large pot to come 3" up sides; fit with thermometer. Heat oil over medium until thermometer registers 350°. Working in 3 batches, gently dip patties in reserved batter, turning a couple times to coat and letting excess drip back into bowl. Fry, turning halfway through and adjusting heat as needed to maintain oil temperature, until golden brown, about 5 minutes. Transfer vadas to paper towels. Between batches, scoop out any stray bits of batter with a slotted spoon and stir into coconut-garlic chutney.

Step 8

(If desired, use slotted spoon to drop beads of remaining batter into oil; fry until crisp and golden brown, about 3 minutes. Transfer fried bits—up to about ½ cup—to coconut-garlic chutney; stir to combine. Discard any remaining batter and/or bits.)

Step 9

Cut a small slit in remaining 10 green Thai chiles (to prevent exploding). Fry chiles until slightly blistered, about 30 seconds. Transfer to paper towels and immediately season with salt.

Step 10

Spoon a tablespoonful of coconut-garlic chutney onto bottom buns of 6 kaiser rolls, split. Top with vadas and another teaspoonful of coconut-garlic chutney, followed by teaspoonfuls of cilantro chutney and tamarind chutney (if desired). Close sandwiches and serve with fried chiles.