Preheat oven to 350°.
To prepare chutney, combine the chutney ingredients in a food processor; process 1 minute or until smooth. Spoon mixture into a bowl; cover and refrigerate.
To prepare samosas, heat 1 tablespoon olive oil in a large nonstick skillet over medium heat. Add onion to pan, and cook for 2 minutes, stirring occasionally. Add carrot, and cook 2 minutes, stirring occasionally. Add peas, mustard seeds, garam masala, and salt; cover and cook 2 minutes. Stir in potatoes; remove from heat.
Working with 1 phyllo sheet at a time, cut each sheet lengthwise into 3 (3 x 14-inch) strips, and coat with cooking spray. (Cover remaining phyllo dough to keep from drying.) Spoon 1 tablespoon potato mixture onto 1 end of each strip. Fold 1 corner of phyllo dough over mixture, forming a triangle; keep folding back and forth into a triangle to end of strip. Place triangles, seam sides down, on a baking sheet. Brush triangles with the remaining 1 tablespoon oil.
Bake at 350° for 23 minutes or until lightly browned. Serve warm or at room temperature with chutney.