Step 1

Slice 1 lb. scrubbed red-skinned potatoes (6–8 small or 3–4 medium) in half with a chef’s knife. Place potatoes in a large saucepan and pour in cold water to cover by 2". (Starting potatoes in cold water ensures even cooking.) Bring to a boil over high heat; reduce heat to medium and simmer until you can easily pierce with the tip of a paring knife, 15–30 minutes, depending on their size. Drain in a colander and let sit until cool enough to handle.

Step 2

Meanwhile, make the hari chutney. Remove tough stems from 1 bunch cilantro and coarsely chop leaves with tender stems until you have ½ cup. Coarsely chop leaves from 1 small bunch mint until you have ½ cup; place in a mini food processor or blender. Set remaining herbs aside for aloo tikki. Cut 1 lime in half and squeeze juice into processor. Remove stem from 1 red or green Thai chile. If you prefer less heat, cut in half lengthwise, then remove ribs and seeds with paring knife. (Wear food-safe disposable gloves and be careful not to touch your eyes!) Add chile, 1 garlic clove, and ½ tsp. Diamond Crystal or ¼ tsp. Morton kosher salt to processor; process, scraping down sides as needed, until chutney is smooth and pourable. If you prefer a thinner chutney, add ice water a tablespoonful at a time (up to 4 Tbsp.), until you reach the desired consistency.

Step 3

For the aloo tikki, place a rack in middle of oven and set a rimmed baking sheet on rack; preheat oven to 200°. Finely chop 1 large shallot, then finely chop reserved cilantro leaves with tender stems until you have ½ cup. Stack 6 reserved mint leaves and roll tightly lengthwise; thinly slice into ribbons. (This is called chiffonade.) Transfer shallots and herbs to a medium bowl.

Step 4

Using your hands, remove skins from cooled potatoes; discard. Grate potatoes on the small holes of a box grater directly into bowl with shallots and herbs. Add 2 Tbsp. rice flour or all-purpose flour (patties won’t be as crispy with all-purpose flour), ½ tsp. cayenne pepper (cut back to ¼ tsp. for less heat), ½ tsp. cumin seeds, ¼ tsp. ground turmeric, and remaining ¾ tsp. Diamond Crystal or ½ tsp. Morton kosher salt. Mix with your hands or a rubber spatula until well incorporated. Turn potato mixture out onto a cutting board and shape into a 2"–3"-diameter log. Be firm and really pack it down—that will prevent the patties from falling apart. Using chef’s knife, cut log into ½"-thick rounds (about 10). Coat hands with oil (to prevent sticking) and form slices into 2½"-diameter patties.

Step 5

Pour vegetable oil into a medium skillet to come ½" up the sides. Heat over medium-high until an instant-read thermometer registers 350° (oil should be shimmering). Working in 2 batches, fry patties, turning once with a slotted spatula, until crispy and golden brown, about 3 minutes per side. (If you're having trouble with the patties falling apart, you can transfer them to the freezer until well-chilled.) Transfer to a paper-towel-lined wire rack to drain; season with salt. Transfer patties to baking sheet in oven to keep warm while you work.

Step 6

Serve with hari chutney for dipping.Do ahead: Hari chutney can be made 3 days ahead. Cover and chill.