Preheat oven to 325F, with rack on middle or lower middle position. Line baking sheets with parchment paper.
In bowl of electric mixer, beat butter and brown sugar until creamy and fluffy, about 1-2 min. Add maple syrup, egg, egg yolk, milk, and vanilla. Beat on low until fully combined.
In a separate bowl, whisk together flour, baking soda, salt, cinnamon, and nutmeg. Add rolled oats to flour mixture and whisk together.
Using wooden or rubber spatula, fold wet ingredients with dry ingredients. Stir in grated apples until fully incorporated. If dough is sticky, chill 30 min to an hour.
Form rounded 1 tablespoons of dough 2 inches apart on parchment lined baking sheets.
Bake 11-13 minutes, or just until lightly golden; don't overbake. Cookies will set upon cooling. Transfer warm cookies to wire rack and let cool.
Place caramels and water in small heavy saucepan. Stir continuously over low heat until melted and smooth. Let rest a bit until it's no longer too hot to handle. Using fork or Ziploc baggie with tiny hole cut out of the corner, drizzle warm caramel over cooled cookies. Be careful - melted caramel is hot!