Bring a large pot of water to boil and prepare an ice bath in a large bowl.
Cut a small ¼-inch deep 'X' in the stem end of each sprout.
Add the sprouts to the boiling water and cook until tender-crisp, about 5 minutes.
Drain the sprouts and immediately plunge them into the ice bath to stop the cooking process.
Once cooled, drain well and cut each sprout in half through the stem.
Heat the olive oil in a large skillet over medium heat.
Place the sprouts in the pan, cut-side down, in a single layer.
Cook without moving until the bottom is nicely browned, about 5 minutes.
Stir in the sliced shallots and minced garlic.
Cook until fragrant and softened, about 1 minute.
Pour in the white wine, vegan Worcestershire sauce, sea salt, and pepper.
Stir to combine, scraping up any browned bits from the bottom of the pan.
Remove from heat and serve immediately.
Don't overcrowd the skillet.
Cook in batches if necessary to ensure each sprout half has direct contact with the pan for optimal browning.