Whisk the chicken broth, soy sauce, balsamic vinegar, 1 Tbs. of the cornstarch, sesame oil, and sugar in a measuring cup. In a large bowl, toss the chicken with 3/4 tsp. salt and a few generous grinds of pepper. Add the remaining 1/4 cup cornstarch and toss with the chicken (you may want to use tongs as the cornstarch has a chalky texture), shaking off any excess cornstarch.
Heat 3 Tbs. of the canola oil in a large (12-inch), heavy-based skillet over medium-high heat until it's shimmering hot. Sauté the chicken, flipping after 2 minutes, until it's lightly browned on two sides, about 4 minutes total (it's all right if the chicken sticks slightly and if the sides of the chicken are still raw).
Add the remaining 1 Tbs. canola oil to the skillet. Add the chiles and their seeds, the ginger, and the whites of the scallions and cook, stirring, for 1 minute.
Add the red pepper and celery and cook, stirring, until they soften slightly, about 2 minutes.
Add the sherry and cook until it almost completely reduces, 30 to 60 seconds, scraping the bottom of the pan to incorporate any browned bits.
Give the chicken broth mixture a quick whisk, stir it into the chicken and vegetables, and bring to a boil (the sauce should immediately thicken). Slice into one of the thicker pieces of chicken to see if it's cooked through. If still pink, reduce to a simmer, cover, and cook a few minutes more.
Serve immediately, sprinkled with the peanuts and scallion greens.