Heat 2 tablespoons of oil in a deep skillet or wok over medium heat.
Add 1 teaspoon of ginger, black pepper, and the minced garlic to the skillet and stir to ensure it is mixed well with the oil.
Add chicken and stir-fry until the chicken is just cooked through. Remove from skillet.
Add an additional 1 tablespoon of oil to the skillet and add the carrots and onions. Stir-fry until the carrots soften and the onions are translucent.
Add chicken back to the skillet and mix with the carrots and onions. Let it cook for 1 – 2 minutes.
Add the cashews and green onions and mix well.
Mix cornstarch, brown sugar, 1/2 teaspoon ginger in a bowl. Add chicken stock and soy sauce. Stir the cornstarch/chicken stock mixture to remove any lumps and pour over chicken.
Stir and let the sauce thicken a bit. If it gets too thick, gradually add more chicken stock.