Preheat your oven to 400 degrees Fahrenheit. While the oven is warming up, wash the Brussels sprouts thoroughly. Trim the woody ends off each sprout and slice them in half lengthwise. If any small leaves fall off during the process, keep them, as these become the crispiest bits after roasting.
Place the halved sprouts onto a large rimmed baking sheet. Drizzle with olive oil and sprinkle with sea salt, black pepper, and smoked paprika. Use your hands or a spatula to toss everything together until each sprout is evenly coated. Spread them out in a single layer, making sure to turn as many as possible cut side down for maximum caramelization.
Slide the baking sheet into the oven and roast for about 20 to 25 minutes. You will know they are ready when the outer leaves are dark brown and crispy, and the flat sides have a deep golden char. Halfway through the cooking time, give the pan a good shake to ensure even browning across all the vegetables.
While the sprouts are in the oven, prepare the glaze in a small mixing bowl. Whisk together the maple syrup, Dijon mustard, and apple cider vinegar until the mixture is smooth and well combined. This glaze can be made ahead of time and kept at room temperature until the vegetables are finished roasting.
Once the sprouts are tender and crispy, remove the pan from the oven. Immediately pour the maple-mustard glaze over the hot sprouts directly on the baking sheet. Use a spatula to toss them until the glaze coats every piece. Transfer to a warm serving bowl and top with toasted pecans if you choose to use them.
