Cut the Brussels sprouts in half. Set them in a large saucepan, and add enough water to just cover.
Bring to a boil, then reduce the heat and simmer, covered, until the Brussels sprouts are bright green and tender but still firm, about 7 minutes.
Heat the oil in a large skillet over medium heat. Add the onion and sauté until translucent, 4 to 5 minutes. Add the garlic and sprouts and continue cooking until the garlic has softened but not browned, about 3 minutes.
Pour in the cider, increase the heat to high, and simmer until it’s reduced by half and the sprouts are tender, adding a splash more water if necessary.