In a small bowl, whisk together the honey, soy sauce, garlic, and ginger until smooth; set aside.

Heat 1 tablespoon of olive oil in a large skillet over medium-high heat.

Place Brussels sprouts in the skillet cut side down in a single layer and cook without stirring for 5 to 7 minutes until deeply browned and caramelized.

Stir the Brussels sprouts and cook for another 2 to 3 minutes until just tender, then transfer them to a plate.

Add the remaining 1 tablespoon olive oil to the skillet and heat until shimmering.

Pat the chicken dry, season with salt and pepper, and add it to the skillet in an even layer.

Cook the chicken for 6 to 8 minutes, stirring occasionally, until browned and cooked through with no pink in the center.

Return the Brussels sprouts to the skillet with the chicken and pour the honey-garlic sauce over the top.

Toss everything to coat and simmer for 2 to 3 minutes, stirring, until the sauce thickens into a glossy glaze.

Remove from heat, sprinkle with sesame seeds and green onions if using, and serve hot on its own or over rice or noodles.