Heat a large cast-iron skillet over high heat. Add carrots and lime; cook, turning occasionally, until charred on all sides, about 7 minutes for carrots and 3 minutes for lime. Remove from skillet; let cool slightly.
Zest and juice lime into a large bowl; whisk in oil, honey, salt, and peppers until smooth.
Shred carrots into bowl with lime mixture; stir in peanuts and chopped basil. Cover and refrigerate for at least 30 minutes before serving. Garnish with basil leaves, if desired.
Recipe by Paula Deen Magazine at https://www.pauladeenmagazine.com/charred-carrot-slaw/