Brussels sprouts with shallots and apples

• 1 pound Brussels sprouts
• 2 large shallots, sliced into 1/4-inch-thick rings
• 2 medium crisp, firm apples (such as Gala, Honeycrisp or Braeburn), cored and cut into 1/2-inch chunks
• 1/2 cup water, divided
• 1/4 cup cider vinegar, divided
• 1/4 teaspoon sea salt
• 1/2 teaspoon freshly ground black pepper
• 4 sprigs fresh thyme

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Rinse Brussels sprouts well and pull off any loose or yellowing leaves. Trim the stem ends and then quarter each sprout. Set aside.

Heat a large high-sided sauté pan over high heat. Add shallots to the very hot pan 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. Add Brussels sprouts, remaining 1/4 cup water, 2 tablespoons vinegar, salt and pepper. Reduce heat to medium, cover and simmer until the sprouts and apples are tender enough to be pierced all the way through with a fork, stirring occasionally, about 15 minutes.

Uncover, stir in remaining 2 tablespoons vinegar and the leaves pulled from sprigs of thyme. Scrape any bits from the bottom of the pan as liquid sizzles and reduces until nearly gone. Transfer to a serving bowl with any of the remaining liquid and serve immediately.