Preheat oven to 350 degrees. Lightly butter an 8 by 8-inch baking dish, line with parchment paper, and butter the parchment. (Buttering the pan helps keep the parchment paper in place when adding the crust.)

With an electric mixer using the whisk or paddle attachment, mix together the butter and brown sugar until well blended. Start on medium speed, increasing to medium-high once it starts to blend together. (Note: mom only had the whisk attachment on her mixer; I’ve tested this recipe with the paddle attachment on my stand mixer, and it works just as well.)

Add the flour and nuts to the bowl. Mix on low speed, gradually increasing speed to medium, until combined. Stop and scrape down the sides and bottom of the bowl a few times. Mixture should resemble coarse crumbs.

Reserve 1/2 cup mixture for topping. Press the remaining crumb mixture evenly into the bottom of the prepared pan. Bake for 10 to 12 minutes or until a light golden brown. Set aside.

In the clean mixer bowl (still using the whisk or paddle attachment), blend the sugar and cream cheese until smooth and creamy.

With the machine running, add the egg, then the lemon juice, zest, milk, and vanilla. Beat until well combined, scraping down the sides of the bowl as needed.

Pour the cheesecake filling evenly over the baked crust, spreading it into an even layer. Sprinkle the reserved crumb mixture evenly over the top.

Bake for 20 to 23 minutes. It will puff up and then settle back down. When done, it should be set around the edges and mostly set in the center when gently pressed. Be careful not to overcook, as the cookies may become dry when cooled.

Cool to room temperature in the pan on a wire rack. Wrap with plastic wrap and refrigerate for at least 2 hours or until well chilled.

For clean slices, cut the bars when cold, using a sharp knife. You may need to clean the knife with a wet cloth a few times.

Store, covered, in the refrigerator.