Cheesy Samosa Puffs

1 lb. russet potatoes (about 2 large), scrubbed
1 Tbsp. plus 1½ tsp. Diamond Crystal or 2¾ tsp. Morton kosher salt, plus more
2 Tbsp. avocado oil or vegetable oil
½ tsp. cumin seeds
½ tsp. mustard seeds
1/3 tsp. asafetida
1 medium serrano chile or 2 green Thai chiles, finely chopped
1 1" piece ginger, peeled, finely chopped
2 Tbsp. ground coriander
½ tsp. ground turmeric
6 oz. cheddar, cut into ¼" cubes
3 Tbsp. coarsely chopped cilantro
1 Tbsp. plus 1½ tsp. fresh lime juice
1 tsp. garam masala
1 tsp. sugar
2 sheets frozen puff pastry (two 14-oz. packages or one 17.3-oz. package), thawed
All-purpose flour (for dusting)
1 large egg, beaten to blend

Place a rack in middle of oven; preheat to 400°. Place potatoes in a medium saucepan and pour in cold water to cover by 1". Season generously with salt and bring to a boil. Reduce heat and simmer until potatoes are very tender, 25–30 minutes. Drain potatoes and let sit until cool enough to handle.
Peel potatoes, then place in a large bowl and mash with a potato masher or fork until mostly smooth with some pea-size pieces remaining.
Heat oil in a medium nonstick skillet over medium. Cook cumin seeds, mustard seeds, and asafetida, stirring, until fragrant, about 10 seconds. Add chile and ginger and cook, stirring, until softened, about 30 seconds. Stir in coriander, turmeric, and 1 Tbsp. plus 1½ tsp. Diamond Crystal or 2¾ tsp. Morton kosher salt; cook, stirring, until fragrant, about 1 minute. Add potatoes and mix until spiced oil is thoroughly incorporated. Return potato mixture to bowl and let cool.
Stir cheese, cilantro, lime juice, garam masala, and sugar into potato mixture. Taste and season with more salt if needed.
Unfold puff pastry sheets on a lightly floured surface and cut into eighteen 2½" squares. Roll out each square to about 4½", then divide between 2 parchment-lined baking sheets.
Working one at a time, brush edges of pastry with egg. Spoon a heaping tablespoonful of potato mixture onto center of each square. Fold pastry in half by bringing one of the top corners up and over filling and matching it up with the opposite bottom corner to make a triangle. Pinch edges together to seal, then crimp with a fork. Brush tops with egg. Chill puffs 15 minutes.
Bake puffs until pastry is golden brown and cheese is melted, 25–30 minutes. (Some cheese may ooze out and that is okay.)
Serve with ketchup, green chutney, or hot sauce for dipping.