Preheat the oven to 350 degrees F (175 degrees C). Line a 9-inch springform pan with parchment paper.
Mix graham cracker crumbs and 2 tablespoons sugar together in a bowl. Mix in melted butter until well combined. Press into the bottom of the prepared pan.
Bake in the preheated oven until firm, about 8 minutes. Remove and let cool. Reduce oven temperature to 300 degrees F (150 degrees C).
Beat labneh in a large bowl with an electric mixer on low speed until fluffy. Add 1 cup sugar gradually, beating until blended. Add eggs one at a time, beating well after each addition. Mix in vanilla extract. Pour batter over the cooled crust.
Cut a single sheet of aluminum foil large enough to surround all sides of the springform pan. Wrap the pan carefully, ensuring all sides are tightly covered. Place the wrapped pan in a deep baking pan; add enough hot water to come halfway up the sides of the pan.
Bake in the preheated oven for 1 hour. Turn off the oven and let the cheesecake settle for 30 minutes, with the door closed. Open the oven door partially and let the cheesecake cool inside for 30 minutes. Remove from the oven and run a knife around the edges. Let cool completely, about 30 minutes. Refrigerate until firm, 8 hours to overnight.
Combine strawberries and 1/3 cup sugar in a blender; blend until smooth.
Bring strawberry mixture to a simmer in a saucepan over low heat; cook and stir for 15 minutes. Remove from heat and let cool. Garnish cheesecake with the sauce.
