Preheat oven to 350 degrees F (180 C). Grease an 8 inch square metal pan or line with non-stick foil.
Beat butter, brown sugar and salt together until creamy. Add flour and stir until it is fully blended – batter will be thick and crumbly. Stir in the nuts. Measure out about 1 cup and set aside. Press remainder into bottom of pan. Bake crust for 15 minutes.
Beat cream cheese and granulated sugar until creamy. Beat in lemon juice and vanilla, then add egg and milk and beat just until smooth.
Pour cheese mixture over baked crust. Sprinkle reserved crumb topping over top. Return to oven and bake for 25 minutes. Let cool on a wire rack, then transfer to refrigerator and chill for at least 2 hours or until ready to serve.