Place the chopped pecans in a dry skillet over medium heat, tossing frequently for 3-5 minutes until fragrant and lightly toasted, then set aside.
Season the chicken breast evenly with the sea salt and black pepper.
Heat the olive oil in a large skillet over medium-high heat. Add the chicken and sear for 6-7 minutes per side until golden brown and cooked through.
Remove the chicken from the skillet and let it rest on a plate.
In the same skillet, add the sliced carrots and a splash of water. Cover and steam for 4 minutes until slightly tender.
Uncover the skillet and stir in the grated ginger, maple syrup, and apple cider vinegar.
Sauté the carrots for another 3-5 minutes, stirring often, until the liquid reduces into a sticky glaze and the carrots are caramelized.
Slice the rested chicken and serve alongside the glazed carrots, garnishing everything with the toasted pecans.