Step 1

Adjust oven rack to middle position and preheat oven to 450°F (230°C). Combine chorizo and olive oil in a medium skillet and heat over medium heat. Cook, stirring, until chorizo is crisped in spots, about 5 minutes. Add shallots and garlic and cook, stirring, until pale golden brown. Add paprika and continue to cook, stirring, until garlic and shallots are browned. (The shallots may lightly char in spots; this is fine.)

Step 2

Strain mixture into a large bowl and reserve solids. Add Brussels sprouts to bowl and toss to coat. Season with salt and transfer to a rimmed baking sheet, arranging sprouts in a single layer, cut side down.

Step 3

Transfer to oven and roast until charred and tender, about 20 minutes.

Step 4

Return to large bowl and add reserved chorizo/garlic mixture. Add sherry vinegar and honey. Toss to combine and serve.