In a bowl, with an electric mixer on medium speed, beat butter and brown sugar until smooth. Stir in flour and walnuts. Reserve 2 cups of the dough; lightly press remaining evenly into a 9- by 13-inch baking pan. Bake in a 325° oven until dry to the touch, about 15 minutes. Let cool 10 minutes.
In a bowl, with an electric mixer on medium speed, beat cream cheese and granulated sugar until smooth. Beat in milk, lemon peel, lemon juice, vanilla, and eggs until smooth, scraping down sides of bowl as needed. Pour cream cheese mixture over crust. Sprinkle reserved dough evenly over the top.
Bake in a 325° oven until a knife inserted into the center comes out clean, about 35 minutes. Let cool completely on a rack, then cover and chill until firm, at least 2 hours, or up to 1 day (see notes). Cut into 12 bars.
Note: Nutritional analysis is per bar.