Our homage to the savory Indian pastries calls for a cumin-studded dough and a hearty potato-and-pea filling. Serve fresh out of the fryer with a duo of homemade chutneys.
Whisk together flour, salt, and cumin. Work in butter with your fingertips until mixture resembles coarse crumbs. Add 1/3 cup water and stir until a shaggy dough forms. Transfer to a clean surface; knead until smooth, about 4 minutes. Cover with a bowl. Let rest 1 hour. (Dough can be made ahead up to this point and refrigerated, wrapped in plastic, up to overnight.)
In a medium saucepan, cover potatoes with 2 inches water. Add 1 tablespoon salt. Bring to a boil, then reduce heat and simmer until potatoes are tender when pierced with the tip of a knife, 4 to 6 minutes. Drain.
Heat a large skillet over medium-high. Swirl in 1/4 cup oil. Add cumin, mustard, and coriander; cook until fragrant and mustard seeds begin to pop, about 1 minute. Add onion, ginger, chile, and garlic. Season with 1 teaspoon salt; cook, stirring frequently, until onion is translucent, about 3 minutes. Add potatoes and cook, stirring and mashing with the back of a fork, until the texture of very chunky mashed potatoes. Add lemon juice, cilantro, and peas. Taste and adjust seasoning with salt. Let cool to room temperature, about 1 hour.
Once dough is rested, roll into a log about 10 inches long. Cut into 10 pieces (each about 1 1/2 ounces). Cover with plastic wrap. Working with one piece at a time on an unfloured surface, roll out to a 6-inch circle. Cut circle in half to create two half-moon shapes. Shape each half-moon into a cone by folding it in half and pinching the straight sides together. Fill each cone with heaping 2 tablespoons filling, then pinch closed to create a stuffed triangle. Repeat with remaining dough and filling.
In a deep, heavy pot, heat remaining 2 quarts oil (it should come 2 inches up sides of pot) to 350 degrees. Working in batches so as not to crowd pot, fry samosas, turning occasionally, until golden brown all over, about 4 minutes. Adjust heat as needed to keep oil temperature between 340 and 360 degrees. Transfer to a wire rack to drain. Serve with chutneys, if desired.