In a bowl, stir cornstarch and yogurt until blended and smooth. Set aside at room temperature.
In a large skillet, heat oil over medium heat until hot but not smoking. Add cumin seeds and cook, stirring, until toasted and fragrant but not yet popping, about 30 seconds. Add onion and cook, stirring, until softened and starting to brown, about 3 minutes. Add garlic, salt and curry paste; cook, stirring, until fragrant, about 1 minute.
Stir in potatoes until coated with spices. Pour in water and cover pan quickly. Reduce heat to medium-low and boil gently, stirring occasionally, until potatoes are tender, 15 to 20 minutes. Uncover and simmer, if necessary, until liquid is absorbed. Season to taste with salt. Let cool completely. Stir in peas and yogurt mixture.
Preheat oven to 425°F (220°C).
Place one sheet of phyllo on work surface, with long side facing you, keeping remaining sheets covered with plastic wrap and a damp cloth. Brush sheet lightly with butter. Cut vertically into four strips. Place a heaping tablespoon (15 mL) of filling about 1 inch (2.5 cm) from bottom of each strip.
Starting at the bottom right corner of strip, fold pastry over filling to the left side, making a triangle. Continue folding from left to right and back all the way along the strip to enclose filling and make a neat triangular bundle (like folding a flag). Tuck end underneath and brush top lightly with butter. Place on baking sheet. Repeat with remaining pastry and filling, placing samosas at least 1 inch (2.5 cm) apart on baking sheets.
Bake one baking sheet at a time in preheated oven until samosas are golden brown and crispy, 12 to 15 minutes.
Serve warm with chutney for dipping. Makes 28 samosas.