Line an 8x8-inch cake pan with parchment paper.
In a large bowl, combine graham cracker crumbs, sugar, and melted butter. Pour the graham cracker mixture into the prepared pan. Press the graham crackers into the bottom of the pan with a measuring cup or glass. Set aside.
In a large bowl, beat cream cheese with an electric mixer on high speed until light and fluffy. Add ½ cup of milk and mix until smooth. Add the remaining milk, pudding mix, sugar, and vanilla extract to the cream cheese mixture. Mix on medium speed for 2 minutes.
Pour cheesecake filling on top of the graham cracker crust. Cover the pan with plastic wrap and chill in the refrigerator until set, 2 hours to overnight.
