Combine the jasmine rice and water in a medium saucepan. Bring to a boil over high heat, then reduce to low, cover, and cook 12–14 minutes until tender. Remove from heat and keep covered. The rice runs in parallel with everything below — that overlap is what keeps this at 30 minutes.

In a large bowl, combine the ground turkey, panko, egg, green onion whites, garlic, ginger, 1 tablespoon soy sauce, salt, and pepper. Mix gently with your hands just until combined — overmixing makes dense meatballs. Roll into about 20 small meatballs, roughly 1 tablespoon each.

Heat the neutral oil in the large skillet over medium-high heat. Add the meatballs in a single layer (work in two batches if the pan is crowded) and cook, turning, until browned on all sides and cooked through, 8–10 minutes total.

Transfer the meatballs to a plate. Add the broccoli to the same skillet with a splash of water (about 2 tablespoons), cover, and steam 2 minutes. Uncover and cook 2 minutes more, stirring, until bright green and crisp-tender.

Whisk together the soy sauce, honey, rice vinegar, ginger, and garlic for the glaze. Pour it into the skillet and bring to a simmer. Stir the cornstarch slurry once more and pour it in, stirring constantly until the sauce turns thick and glossy, about 1 minute. Return the meatballs to the pan and toss to coat.

Fluff the rice with a fork. Serve the glazed meatballs and broccoli over the rice, spooning extra sauce from the pan over everything. Finish with green onion greens and toasted sesame seeds.