Roasted Brussels Sprouts with Gochujang Brown Butter

3 lb. brussels sprouts, trimmed, halved if large
2 Tbsp. extra-virgin olive oil
Kosher salt, freshly ground pepper
½ cup coarsely chopped walnuts (optional)
6 Tbsp. unsalted butter
⅓ cup gochujang (Korean hot pepper paste, such as Mother-in-Law’s)
2 Tbsp. pure maple syrup
3 scallions, thinly sliced, divided
½ lemon
Flaky sea salt

Place racks in upper and lower thirds of oven and set a rimmed baking sheet on each; preheat oven to 500°. Toss brussels sprouts with oil in a large bowl to coat; season with kosher salt and pepper. Carefully (baking sheets will be hot!) divide brussels sprouts between baking sheets and spread out in a single layer; reserve bowl. Roast, rotating baking sheets top to bottom and front to back halfway through, until brussels sprouts are charred in spots and tender, 16–18 minutes.
Meanwhile, if using walnuts, toast in a dry medium skillet over medium heat, tossing often, until fragrant and slightly darkened, about 4 minutes. Transfer to a small bowl and let cool.
Cook butter in a small saucepan over medium-low heat, swirling occasionally, until milk solids are a deep amber color and butter smells very nutty, 5–8 minutes. Remove from heat and stir in gochujang and maple syrup. Season with kosher salt and pepper.
Combine brussels sprouts, half of walnuts, and half of scallions in reserved bowl; add brown butter mixture and toss to coat. Transfer to a platter and scatter remaining walnuts and scallions over. Finely grate lemon zest on top; sprinkle with sea salt.