Place a large rimmed sheet pan on the upper rack and heat the oven to 425°F. A preheated pan helps the sprouts brown deeply.
Make the glaze: In a small saucepan, whisk together the balsamic, honey, Dijon, soy sauce, garlic, red pepper flakes, and 1/4 tsp of the salt. Bring to a gentle simmer over medium heat and cook, stirring occasionally, until slightly syrupy, 3–4 minutes. Remove from heat and whisk in the butter until glossy. Keep warm on the lowest heat setting.
Toss the Brussels sprouts with the olive oil, remaining 1 tsp salt, and the black pepper until evenly coated.
Carefully pull the hot pan from the oven. Spread the sprouts cut-side down in an even layer (work quickly to maintain heat). Return to the oven and roast until the cut sides are well caramelized and the centers are tender, 18–22 minutes.
Transfer the roasted sprouts to a large bowl. Drizzle over about half the warm glaze and toss to coat. Add more glaze to taste; you may not need it all.
Finish with chives and lemon zest. Serve right away with any remaining glaze on the side for extra drizzling.