1. Heat a large high-sided skillet over high heat. Add shallots and cook, stirring constantly for 2 minutes. Add apples and 1/4 cup water, scraping any brown bits from the bottom as the water sizzles. Cook until the liquid reduces by half, about 2 minutes.
2. Add Brussels sprouts, another 1/4 cup water, 2 tablespoons vinegar, salt and pepper. Reduce heat to medium, cover and simmer until sprouts and apples are just tender, stirring occasionally, about 15 minutes.
3. Uncover, stir in remaining 2 tablespoons vinegar and thyme. Scrape any bits from the bottom of the pan and continue to cook until the liquid has evaporated. Transfer to a serving bowl with any of the remaining liquid and serve immediately.

To make AIP friendly omit: Black Pepper