Heat 2 teaspoons canola oil in a large skillet over medium-high heat. Add onion, carrots, and cabbage; saute until slightly soft, about 3 minutes. Transfer to a large bowl; cool for 15 minutes. Add chicken, brown sugar, sesame seeds, sesame oil, five-spice powder, garlic, ginger, salt, and pepper. Mix until filling is well combined.
Separate and place wonton wrappers onto your work surface. Spoon about 1 1/2 teaspoons of the filling onto the center of each wrapper. Use your finger or a pastry brush to lightly moisten edges with water. Fold one corner over the filling onto the opposite corner to form a triangle. Fold 2 corners over to meet in the center; press together, squeezing out as much air from the center as you can.
Preheat oven to 200 degrees F (95 degrees C). Set a wire rack on a baking sheet.
Heat 1 tablespoon oil in the same skillet over medium heat. Add 6 to 8 potstickers; cook until golden brown, flipping once halfway, 4 to 5 minutes. Add 1 1/2 tablespoons chicken broth to the skillet. Steam, covered, until potstickers are no longer pink on the inside, about 1 minute. Transfer to the wire rack.
Place baking sheet in the preheated oven to keep potstickers warm. Cook remaining potstickers with the remaining oil and chicken broth.