Cut the asparagus into 1- to 1-1/2 inch long pieces and set aside, along with the snap peas.
In a medium bowl, combine the chicken, honey, ginger, garlic and 1 tablespoon of the soy sauce; mix well.
In a small bowl, combine the rice vinegar, sesame oil, chile-garlic sauce, peanut butter and the remaining 1 tablespoon soy sauce. Whisk well to combine.
In a large (12-inch) skillet or wok, heat the oil over medium–high. Place a dinner plate lined with a paper towel near the stove.
When the oil is shimmering, add the chicken mixture and, working quickly, smear it into a roughly even layer that covers the surface of the pan. Cook for 2 to 3 minutes without disturbing, until the edges are nicely browned on the bottom.
Stir the chicken, breaking it up into bite-size pieces and cook, stirring occasionally, for 3 to 5 minutes, until cooked through and deeply caramelized in spots. Using a spatula or slotted spoon, transfer the chicken to the prepared plate.
Reduce the heat to medium and add the asparagus and snap peas. Cook, tossing often, until the vegetables are charred and crisp tender, 3 to 4 minutes. (If the pan begins browning, reduce the heat further.)
Off the heat, return the pork to the pan and toss. Add the reserved vinegar mixture to the skillet and stir, scraping the browned bits from the pan.
Serve over rice.