Preheat the oven to 425°F. Cut a 1-inch top off each apple, and core the apples. Arrange the apples cut side up in a glass baking pan 2 or 3 inches deep and large enough to hold the apples in a single layer. Pour the cider over the apples. Sprinkle each apple with cinnamon. If desired, top each apple with a pat of butter. Pour ¼teaspoon vanilla extract on top of each apple and pour the remaining ½teaspoon into the cider in the pan. Cover tightly with foil.
Bake for 30 minutes, then uncover and baste. Replace the foil and continue baking for 15 to 30 minutes, until cooked to the desired softness.
Combine the yogurt, honey, and cinnamon, transfer the apples to individual bowls, and top the apples with the yogurt mixture.