Preheat the oven to 425°F (220°C). Line or spray a large nonstick baking sheet 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 coated chicken pieces on one side of the prepared baking sheet in a single layer, leaving space for the broccoli.
Bake the chicken for 10 minutes, then remove the pan and flip the chicken pieces.
Add the broccoli florets to the empty side of the pan, drizzle with 2 teaspoons sesame oil, and season with the remaining 1/2 teaspoon kosher salt and pepper to taste.
Return the pan to the oven and bake until the chicken is cooked through and broccoli is tender, about 10 more minutes.
While the chicken and broccoli finish cooking, whisk together the honey, sriracha, seasoned rice vinegar, and 1 teaspoon sesame oil in a medium bowl until smooth.
When the chicken is done, transfer it to the bowl with the sauce and toss to coat evenly.
Divide the cooked brown rice among 4 bowls, top with the sauced chicken and roasted broccoli, and garnish with sliced scallions and sesame seeds.