You want to start off with pretty thinly sliced chicken breasts. Aim for 1/3-inch thick slices. 1/2-inch slices are okay, but you'll need to cook the chicken for a few more minutes. Cut each slice of chicken breast into 1-inch wide strips.
In a medium bowl, mix the apple cider, lime juice, fish sauce, ginger, sesame oil, lemongrass, and garlic together. Add the chicken breasts and cover the bowl with plastic wrap. Refrigerate overnight.
Take marinated chicken out of the refrigerator. Thread chicken strips through the soaked skewers.
Heat a large skillet with 1 1/2 to 2 tablespoons of olive oil over medium to medium-high heat. Place about half of the chicken skewers on the skillet. Cook each side for about 3 minutes. If you are working with thicker chicken strips, you'll want to cook each side for 4 to 5 minutes. Set the first batch of cooked chicken onto a plate to cool. Add another 1 1/2 to 2 tablespoons of oil into the skillet. Place the remaining chicken in the skillet and cook each side for 3 minutes.
While the chicken is cooking, prepare the dipping sauce. Blend dipping sauce ingredients together until smooth. Top with red pepper flakes, if desired.
Let the chicken rest for a few minutes before serving. Enjoy with the dipping sauce.
Refrigerate leftover chicken for 4 to 5 days. Refrigerate dipping sauce for 1 week. The sauce will be thick when it's refrigerated. Leave it out in room temperature for 15 minutes before using it again or dip the container in a bowl of warm water for 5 minutes.