Heat 2tsp oil in a saute pan, add mustard seeds and once they start spluttering add the onions and green chilies. Cook till onions are lightly browned around the edges.
Add carrot and tomatoes, cook for 3~4 minutes or until tomatoes are mushy and carrots change color. Let the mixture cool, then grind along with salt.
Heat 1tsp oil in a small saucepan; add the mustard seeds, dry red chili and curry leaves. Once the seeds start to splutter, add the tempering to the chutney.