Place the potatoes and 2 tablespoons of the salt in a 4-quart pot. Cover with cold water by 1-inch and bring to a boil over high heat. Reduce the heat to maintain a steady simmer and cook for 8 minutes, or until the potatoes are tender but not mushy. (When pierced with a paring knife, there should be a slight yield.) Drain and rinse under cold water.
When the potatoes are cool enough to handle, grate them on a box-style grater placed over a large mixing bowl, discarding any skins that don't make it through the grater. Add the remaining salt, shallot, chili powder, coriander, cumin, lemon juice, cilantro, and mint to the grated potatoes. Mix well with your hands or a silicone spatula.
Place the panko in a shallow pie plate or baking dish. Roll the potato mixture into 1/2-inch balls, 12-13 grams each (a digital scale is helpful here), then roll in the panko to coat.
Place the tots on a parchment-lined half-sheet pan and refrigerate for 30 minutes. The tots may be refrigerated overnight covered with plastic wrap.
To cook, add the oil to a 5-quart Dutch oven or heavy bottom pot. If using a clip-style candy/deep fry thermometer, attach the clip to the rim of the pot and bring the oil to 375℉ over medium-high heat. Have a second half-sheet pan or large plate with several layers of paper towels nearby your cooktop.
Retrieve the tots from the fridge and load 8-10 at a time, into a spider or large slotted spoon. Carefully lower them into the hot oil and fry for 2 minutes. Remove with the spider or slotted spoon and drain on the paper towels. Season with salt. Repeat with the remaining tots.
Serve hot with Indian-Style Spiced Ketchup, if desired.