Step 1
Place 1 cup cylindrical rice cakes (about 2½” long) in a medium bowl; pour in cool water to cover. Let soak 20 minutes. Drain and pat dry. Cut rice cakes in half; set aside.
Step 2
Meanwhile, combine 1¼ lb. skinless, boneless chicken thighs and/or breasts, cut into 1″ pieces, one 1″ piece ginger, peeled, finely grated, 2 garlic cloves, finely grated, 1 Tbsp. mirin, and ½ tsp. Diamond Crystal or ¼ tsp. Morton kosher salt in a medium bowl; season with freshly ground pepper. Mix well; set aside.
Step 3
Whisk 8 garlic cloves, coarsely chopped, ¼ cup soy sauce, 2 Tbsp. sugar, 1 Tbsp. apple cider vinegar, remaining 1 Tbsp. mirin, and ½ cup water in a small bowl until sugar is dissolved. Set dressing aside.
Step 4
Place 1 cup potato starch or cornstarch and 1 tsp. Diamond Crystal or ½ tsp. Morton kosher salt in a large bowl; season generously with pepper and whisk to combine. Remove reserved chicken from bowl, letting any marinade drip back into bowl; place in bowl with seasoned potato starch. Gently toss to coat, pressing down into mixture and turning to cover every surface; set aside.
Step 5
Pour vegetable oil (about 1½ cups) into a medium stainless-steel or cast-iron skillet to come ½” up sides and heat over medium-high until an instant-read thermometer inserted into oil registers 350°. Fry half of chicken in a single layer until golden brown and crisp underneath, 2–3 minutes. Turn over; fry until golden brown and crisp on the other side, about 2 minutes. Transfer to a wire rack set inside a parchment-lined baking sheet; season with salt. Using a slotted spoon, remove any dark bits from oil and return oil to 350°; repeat with remaining chicken. Bring oil back to 350° again, then return all of the chicken to pan. Fry until deep golden brown, 1–2 minutes. Transfer back to rack.
Step 6
Stir remaining 1 tsp. potato starch or cornstarch and 2 Tbsp. water in a small bowl until starch is dissolved. Set slurry aside.
Step 7
Heat remaining 1 Tbsp. vegetable oil in a large skillet over medium. Add reserved rice cakes and cook, stirring, until golden brown in spots, 2–3 minutes. Transfer to rack with chicken. Reduce heat to medium-low and carefully pour in reserved dressing. Cook, stirring with a heatproof rubber spatula, until sugar is dissolved. Add reserved slurry (give it a quick stir if it has separated); cook, stirring constantly, until dissolved into sauce. Continue to cook sauce, stirring occasionally, until a line drawn through sauce with spatula holds, 30–60 seconds more. Reduce heat to low; add chicken and rice cakes and toss until every piece is coated with some sauce; remove from heat.
Step 8
Arrange chicken and rice cakes on a large plate; top with chopped salted roasted peanuts and chopped cilantro. Serve with toothpicks or skewers if desired.
