1. Prepare an ice bath. In a large stockpot, bring 4 quarts of heavily salted water to a boil. Working in batches, blanch the brussels sprouts until tender, about 3 to 5 minutes per batch, then transfer to the ice bath. When all the brussels sprouts have been blanched, strain them in a colander and set aside.

2. In a skillet, heat the butter over medium heat, swirling occasionally, until deep golden, about 5 minutes. Remove the butter from the heat and let cool slightly.

3. In a small bowl, whisk the egg yolk with the vinegar and water. Slowly whisk in the warm brown butter and season with salt and pepper. Cover the bowl and set aside in a warm place.

4. Heat about 1 inch of vegetable oil in a skillet over medium heat until the oil reaches 300˚. Fry the sage leaves until crisp, then transfer to paper towels to drain.

5. Drain all but 1 tablespoon of the oil from the skillet and return it to the stove. Heat the oil until nearly smoking, then add the brussels sprouts cut side down. Sear the brussels sprouts over medium-high heat until golden, about 2 to 3 minutes per side. Season with salt and pepper and transfer to a serving dish. Whisk the brown-butter sauce and pour over the sprouts. Garnish with the fried sage and serve immediately.