Preheat the oven to 350 degrees F (175 degrees C).

Mix flour, walnuts, butter, and brown sugar together in a bowl. Line a 9x13-inch baking pan with half the crust mixture.

Bake in the preheated oven until browned, about 15 minutes. Remove crust and leave oven on.

Mix cream cheese and white sugar together in another bowl using an electric mixer until blended. Add eggs, milk, lemon juice, and vanilla extract; mix until blended. Pour on top of the baked crust. Sprinkle with remaining crust mixture.

Bake in the hot oven until set, about 25 minutes.