Combine apples, brown sugar, cinnamon, nutmeg, lemon juice, and water in a small saucepan.

Cook over medium heat, stirring, until apples soften and sauce thickens, about 8–10 minutes.

Let compote cool slightly. Taste and add a pinch more sugar if needed.

Spoon yogurt into bowls and top with warm compote.

Sprinkle nuts or granola if using. Serve warm or room temp.