This dish is very easy to make. Caramelized in sausage drippings, the sprouts stay lighter than expected thanks to some quickly pickled red onion and lots of fresh parsley.
Toss onion in vinegar and season with salt and pepper. Mix thoroughly and set aside.
Heat 1 tablespoon oil in a large skillet (at least 12-inches) over medium–high heat. Add sausage, using a wooden spoon or spatula to break it up into smaller pieces. Cook, stirring occasionally, until sausage is cooked through, browned and crispy, 8 to 10 minutes. Using a slotted spoon, remove sausage from skillet, leaving any fat behind. Set aside.
Add remaining 2 tablespoons olive oil to the skillet along with brussels sprouts. Season with salt and pepper and shake skillet so that most of the sprouts land cut-side down, turning some over with a fork, if necessary. Cook, without stirring, until brussels sprouts are well browned on one side, 5 to 8 minutes. Shake skillet to continue to brown sprouts all over, another 5 to 8 minutes. Add sausage back into skillet and stir to combine.
Remove from heat and add onions and any vinegar left over, tossing to coat. Season with salt and pepper, add parsley and serve.