Preheat the oven to 475°.
Bring a large pot of water to a boil. Trim the bottoms of the Brussels sprouts and halve them lengthwise. Salt the water, add the Brussels sprouts, and parboil until crisp-tender, about 5 minutes. Drain and dry on a kitchen towel. Transfer to a baking sheet. Dress with 3 tbsp. oil, then season with salt, pepper, and the smoked paprika. Roast the Brussels sprouts, cut-side down, until golden and tender, about 20 minutes.
Meanwhile, in a large skillet, heat the remaining 1 tbsp. oil, one turn of the pan, over medium. Add the chorizo and cook until the fat begins to render, a few minutes. Add the shallots and garlic and cook, stirring often, until the vegetables soften, 2 to 3 minutes.
Add the Brussels sprouts to the skillet. Dress with the vinegar and honey; season.