Preheat oven to 350F
Thaw the phyllo dough following the directions on the package. Unroll and cover with a damp paper towel to prevent drying.
Place the potatoes in a saucepan, cover with water, and bring to a boil.
Boil the potatoes until fork tender, about 10 minutes. Mash the potatoes until smooth.
Add the carrots, corn, peas, garlic powder, cumin, turmeric, and salt to the mashed potatoes and stir to mix well.
Place one phyllo sheet down and brush with melted butter using a pastry brush. Repeat with two more sheets so you have 3 sheets of phyllo stacked in front of you. Cut lengthwise into 3 strips.
Place 1 tablespoon of the filling at the bottom end of each strip. Fold the corner of the dough over the filling to form a triangle. Continue to fold the triangle over itself. Brush the top with melted butter. Repeat with remaining phyllo and filling.
Place triangles, seam side down, on a baking sheet. Bake for 30 minutes, until golden brown.