Preheat the oven to 475°F and line a baking sheet with parchment paper or lightly oil it.
In a bowl, combine the cubed chicken, beaten egg, and a pinch of black pepper; toss to coat.
In a separate bowl, stir together the flour, ground ginger, and a pinch of salt. Working in batches, dredge the egg-coated chicken in the flour mixture until evenly coated and place the pieces on one side of the prepared baking sheet.
Drizzle about 2 tablespoons of the oil over the chicken. On the other side of the sheet, toss the broccoli florets, sliced bell peppers, and quartered shallots with the remaining 2 tablespoons oil.
Bake at 475°F for 15 minutes.
While the sheet is baking, combine the sweet Thai chili sauce, soy sauce, apple juice, rice vinegar, ketchup, peanut butter, sliced jalapeño, and grated garlic in a medium saucepan. Bring to a boil over medium-high heat, then simmer and boil gently for 5–8 minutes until the sauce thickens and reduces by about one-third.
Reduce the oven temperature to 400°F. Remove the sheet pan from the oven and pour half of the sauce over the chicken, tossing to coat; toss the vegetables as well.
Return the sheet pan to the oven and bake at 400°F for about 3 minutes, just until the sauce is glossy and coats the chicken. Watch carefully to prevent burning.
Serve the chicken and remaining sauce over bowls of rice with cilantro, and plate the roasted vegetables on the side.
