Combine water, sugar, vanilla, and lemon juice in a saucepan and bring to a simmer.

Add apple halves, cut side down. Simmer gently 8–10 minutes until tender but not mushy.

Remove apples with a slotted spoon. Keep poaching liquid warm.

If using butter, stir it and a pinch of salt into the liquid for a thin syrup.

Plate apples, spoon syrup over them, and sprinkle granola on top.

Serve warm or at room temperature, with yogurt if desired.