Cook the rice according to package instructions, then fluff with a fork and set aside, keeping it warm for assembling the bowls.
Cut the broccoli into bite-size florets and slice the chicken breasts into even strips so they cook quickly and evenly.
In a bowl, toss the chicken with salt, pepper, smoked paprika, garlic powder, onion powder, and dried oregano until all pieces are well coated.
Heat the olive oil in a large skillet over medium-high heat, add the seasoned chicken, and cook until golden on the outside and cooked through in the center.
Transfer the cooked chicken to a plate, leaving any browned bits in the skillet to flavor the sticky sauce.
In the same pan, whisk together soy sauce, honey, garlic, ginger, and sesame oil, then bring to a gentle simmer.
Stir in the cornstarch slurry and cook, stirring often, until the sauce thickens and turns glossy enough to coat the back of a spoon.
Add the cooked chicken back into the skillet and toss until every piece is coated in the sticky glaze, then simmer for 1–2 minutes.
Meanwhile, steam or sauté the broccoli florets just until crisp-tender and bright green, then season lightly with salt.
For an optional drizzle, stir together the Greek yogurt or mayonnaise with sriracha and a splash of water until smooth and pourable.
Assemble the bowls by adding a scoop of rice to each, topping with sticky chicken and broccoli, then finishing with the spicy drizzle, green onions, and sesame seeds.