Preheat the oven to 350°F (175°C).

In a bowl, mix graham cracker crumbs, 2 tablespoons granulated sugar, and melted butter. Press mixture into the bottom of a greased baking dish.

In another bowl, beat cream cheese and ¾ cup sugar until smooth. Add the egg and vanilla extract, and mix until well combined.

Pour the cream cheese mixture over the crust in the baking dish.

In a separate bowl, combine sliced strawberries, lemon juice, ½ cup light brown sugar, cornstarch, oats, 1 cup light brown sugar, ground cinnamon, and salt. Mix until strawberries are coated.

Spread the strawberry mixture over the cream cheese layer.

Dot the top with cold butter.

Bake for approximately 85 minutes, or until the filling is set and the edges are golden.

Allow to cool before cutting into bars.