Make The Dough: Pulse Flour, Butter, And Salt In A Food Processor Into Pea-Size Crumbles. Add Water; Pulse Until Dough Forms. Divide Into 12 Balls; Chill 1 Hour.
Make The Filling: Boil Potatoes And Carrots In A 4-Qt. Saucepan Of Salted Water Until Tender, 8–10 Minutes. Drain; Coarsely Mash.
Add 2 Tbsp. Oil To Pan; Heat Over Medium-High. Cook Cumin Seeds Until They Pop, 1–2 Minutes.
Add Onion And Ginger; Cook Until Golden, 4–6 Minutes.
Let Cool; Stir Into Potato Mixture With Peas, Cilantro, Mint, Garam Masala, Chiles, And Salt.
Form And Fry Samosas: Working With 1 Ball At A Time, Roll Dough Into A 6" Round; Cut In Half.
Gather Straight Edges Of 1 Half-Round Together, Overlapping By 1⁄4" To Form A Cone. Moisten Seam With Water; Press To Seal.
Filling Into Cone. Moisten Edges Of Cone With Water; Pinch To Seal. Heat 2" Oil In A 6-Qt. Saucepan Until A Deep-Fry Thermometer Reads 350°.
Fry Samosas Until Crisp, 8–10 Minutes.
Drain On Paper Towels; Serve With Chutneys If You Like.
