Preheat your oven to 325°F (160°C).
Line your 9x9-inch baking pan with parchment paper, leaving some overhang on the sides.
In a mixing bowl, combine the melted salted butter and packed light brown sugar. Mix until well combined. Add the all-purpose flour and finely ground walnuts, stirring until a crumbly dough forms.
Transfer the crust mixture into the prepared baking pan. Press it down firmly and evenly across the bottom. Bake for about 10 minutes or until lightly golden.
In another mixing bowl, beat the cream cheese with an electric mixer until smooth. Gradually add the granulated white sugar, mixing until combined. Add the egg, milk, lemon juice, and vanilla extract. Beat until creamy and smooth.
Once the crust has cooled slightly, pour the cheesecake filling over the crust. Use a spatula to spread it evenly. Bake for an additional 20-25 minutes until the edges are set and the center is slightly jiggly.
Remove from the oven and let it cool to room temperature. Refrigerate for at least 2 hours or until fully chilled.
Using the overhanging parchment paper, lift the cheesecake out of the pan. Cut into squares and serve.
