In a bowl, beat butter and granulated sugar until fluffy. Beat in eggs and vanilla.
In another bowl, whisk flour, baking powder, spices, and salt. Fold into butter mixture.
Fold in apples and lemon zest. Chill 1 hour.
Preheat the oven to 350°F. Line baking sheets with parchment. Roll dough into balls and coat in brown sugar. Place 2 inches apart on prepared baking sheets. Sprinkle lightly with Demerara sugar.
Bake for 15-18 minutes until lightly browned. Transfer to wire racks to cool.
Once fully cooled, drizzle cookies with warm caramel sauce.