Bring a medium saucepan of salted water to a boil. Add the potatoes, lower the heat and simmer until tender, about 15 minutes. Drain and mash.
Meanwhile, in a heavy skillet, toast the cumin and turmeric over medium heat, stirring occasionally, until fragrant, about 2 minutes. Add the oil, onion, garlic and salt and cook, stirring, until the onion is softened, about 7 minutes. Stir in the peas and carrots. Remove from the heat and stir in the mashed potatoes.
Position a rack in the center of the oven and preheat to 400 degrees . Line a baking sheet with parchment paper. Brush 1 phyllo sheet with melted butter. Top with another phyllo sheet; brush lightly with butter. Cut lengthwise into five 2 1/2-inch-wide strips. Place 1 heaping tablespoon of the vegetable mixture at the end of each strip. Working with 1 strip at a time, fold the corner over the filling to enclose, forming a triangle; continue folding the strip like a flag, keeping the triangle shape. Place the resulting bundles seam side down on the baking sheet. Repeat with the remaining phyllo sheets and filling. Bake until golden, about 10 minutes.
In a small bowl, stir the apple butter with 3/4 cup water. Serve warm or at room temperature with the bundles.