Preheat the oven to 425°F (220°C). Line a large nonstick baking sheet or spray it generously with olive oil spray.
Place the diced chicken in a bowl and toss with the beaten egg white until coated, then add the cornstarch and 3/4 teaspoon kosher salt and toss to coat evenly.
Arrange the chicken pieces on one side of the prepared baking sheet in a single layer so they have room to roast; bake for 10 minutes.
While the chicken bakes, toss the broccoli florets with 2 teaspoons sesame oil and the remaining 1/2 teaspoon kosher salt and a pinch of black pepper to taste.
Remove the pan from the oven, flip the chicken pieces, add the broccoli to the other side of the sheet, and return to the oven; bake until chicken is cooked through and broccoli is tender, about 10 more minutes.
Meanwhile, whisk together the honey, sriracha, seasoned rice vinegar, and 1 teaspoon sesame oil in a medium bowl until smooth.
When chicken is done, transfer it to the bowl with the sauce and toss to coat evenly.
Divide cooked brown rice among 4 bowls, top each with sauced chicken and roasted broccoli, then garnish with sliced scallions and sesame seeds.