Cream softened butter and brown sugar in a bowl until light and fluffy.

Add flour and chopped nuts to the mixture and mix well to form the crust.

Reserve 1 cup of the crust mixture for topping.

Press the remaining crust mixture into a greased 8-inch square baking pan.

Bake the crust at 350°F (175°C) for 12 minutes.

While the crust is baking, prepare the cheesecake filling.

In a separate bowl, combine softened cream cheese, sugar, egg, milk, lemon juice, and vanilla.

Mix the filling until smooth and creamy.

Pour the cheesecake filling over the partially baked crust.

Sprinkle the reserved crust topping evenly over the filling.

Bake the cheesecake cookies at 350°F (175°C) for an additional 15-20 minutes, or until the filling is set.

Let the cheesecake cookies cool completely before cutting into squares.