Heat a large cast-iron skillet over high heat. Add carrots and whole lime; cook, turning occasionally, until charred on all sides, about 3 minutes for lime and 7 minutes for carrots. Remove from skillet; let cool slightly.
Zest and juice lime into a large bowl; whisk in oil, mustard, agave, salt, black pepper, and coriander until smooth.
Shred carrots into bowl with lime mixture; stir in green onion, almonds, apricot, and serrano pepper, if using. Cover and refrigerate for at least 30 minutes before serving. Fold in basil just before serving.
Recipe by Southern Lady Magazine at https://southernladymagazine.com/charred-carrot-slaw-recipe/