Make filling: In a dry frying pan (not nonstick), toast cumin and coriander seeds over medium-high heat until fragrant, about 2 minutes. Let cool, then grind in a spice grinder; set aside.
Whirl garlic and ginger in a food processor until well minced (you should have about 1/2 cup total). Add 1/4 cup water and blend into a paste, scraping inside of bowl as needed. Transfer paste to a small bowl; set aside. Without cleaning bowl of food processor, add onion and pulse until finely chopped.
Heat oil in a large deep pot over medium-high heat. Add three-quarters of onion and fry until beginning to brown on the edges, about 4 minutes. Add ground cumin and coriander, turmeric, chili, and salt and cook, stirring, about 1 minute. Stir in garlic-ginger paste and cook, stirring occasionally, about 2 minutes.
Add lamb and stir to break up meat and thoroughly coat with seasonings. Reduce heat to medium and cook, stirring occasionally, until lamb is no longer pink, about 5 minutes (if using fresh peas, add about halfway through cooking lamb).
Stir in remaining one-quarter of onion and the peas (if using frozen). Cook until just heated through, about 2 minutes. Remove from heat and let cool completely.
Meanwhile, make dough: In a large bowl, whisk flour with salt and ajwain seeds if using. Mix butter into flour. Drizzle about 1/2 cup warm water over dough and mix in with your hands until dough comes together. If it seems dry, drizzle in 1 to 2 tbsp. additional water. Knead dough until smooth, about 5 minutes. Divide dough into 6 pieces, roll each piece into a ball, then roll each ball out to a 1/8-in thickness (about an 8-in. round), rolling edges a little thinner. Cut each round in half.
Working with a half at a time and keeping the rest covered with a damp kitchen towel to stay moist, moisten half of the straight edge from center to corner with water. Bring the two corners together and form into a cone, overlapping the wet edge onto the dry and pinching to seal; this is the center seam. Pinch bottom of cone to seal as well.
Line a baking sheet with parchment paper. Holding cone upright like an ice cream cone, spoon in a third to a half cup filling. Press filling down gently to eliminate air pockets and allow edges of dough to meet over filling. Moisten inner side of one top edge with water, then pinch top edges together into a ridge to seal; fold corners back and away from center seam.
Lay samosa on baking sheet with tip farthest from you and center seam up. Roll samosa forward so it's upright, with the ridge (now on bottom) extending out toward you like a fringe. Tap samosa gently on its bottom to make it flat and create a pyramid. Repeat with remaining dough and filling.
Meanwhile, fill a large deep pot with enough vegetable oil to come 4 in. up the sides. Heat over medium-high heat until a deep-fry thermometer registers 360°. Fry samosas in batches of 3, turning often, until pale golden, about 5 minutes. Transfer to a baking sheet and let rest 10 minutes, then reimmerse in hot oil and fry until well browned, about 5 minutes (the resting and double frying helps the crust bubble appetizingly). Drain on paper towels.
Serve warm or at room temperature, with cilantro chutney if you like.
*Ground Indian red chili is a mixture of various hot red chiles. Maida is a wheat flour similar to all-purpose but more finely milled; it produces a flaky but sturdy crust. All-purpose will be slightly less flaky and more sturdy, and pastry flour will be very flaky but more delicate. Aromatic ajwain (sometimes spelled ajowan) seeds taste like thyme with a hint of celery. Find them all at Indian markets or at khanapakana.com.
Make ahead: Filling and dough, up to 2 days, chilled (let dough come to room temperature before rolling). Formed unfried samosas, up to 1 day, chilled, and up to 3 months, frozen. Samosas can also be partly fried (until pale golden), up to 2 days, cooled and chilled, then fried at 375°, or baked in a 350° oven for 15 minutes, until medium golden.