1. Fill a large bowl with ice and water and set aside. Cook the Brussels sprouts in a large pot of liberally salted boiling water over high heat until the sprouts are light green, 3 to 4 minutes. Using a slotted spoon, transfer the sprouts to the ice-water bath and cool for 10 minutes. Drain and halve lengthwise.

2. In a large skillet set over high heat, heat 1 tablespoon of the olive oil until smoking, about 3 minutes. Add the mushrooms and cook, without stirring, for 1 minute, then shake the pan and continue to brown the mushrooms for 2 minutes more. Season with salt and pepper; add 1 tablespoon of the sherry vinegar and stir with a wooden spoon, scraping up the browned bits from the bottom of the pan. Remove the mushrooms from the pan and set aside to cool on a baking sheet lined with a paper towel.

3. Set the skillet back over high heat and add the remaining teaspoon of olive oil. Place the Brussels sprouts in the pan, cut side down; season with salt and pepper and cook until brown, 5 to 7 minutes. Add the butter, garlic, red pepper flakes and the reserved mushrooms and cook until the butter is browned, about 1 minute. Stir in the honey and chestnuts, season with salt and pepper add the remaining 1 tablespoon of sherry vinegar and the water and stir to combine. Transfer to a serving dish, finish with sea salt and serve hot.