Preheat the oven to 350°F. Line a 9-inch × 9-inch baking pan with parchment paper and set aside.

Combine graham cracker crumbs and sugar in a medium bowl. Pour in the melted butter and mix well.

Transfer the crust mixture to the prepared baking pan and press it into an even layer. Bake for 8 minutes.

While the crust is baking, beat together the cream cheese, granulated sugar, egg, and vanilla extract until smooth.

In a medium saucepan, add strawberries and lemon juice. Cook over medium-high heat until the strawberries burst and juice forms, about 5 to 7 minutes.

Mix the brown sugar and cornstarch in a separate bowl, then stir into the strawberry mixture, cooking for an additional 2 minutes until thickened. Remove from heat.

To make the oatmeal crumble, combine oats, brown sugar, cinnamon, and salt in a large bowl. Cut in cold butter until it resembles tiny pebbles.

Pour the cheesecake mixture over the crust and spread evenly. Top with the strawberry filling, then sprinkle the oatmeal crumble on top.

Bake for 50 to 70 minutes until the top is golden brown.

Let cool in the pan on a wire rack for 30 to 60 minutes, then refrigerate for at least 4 hours before slicing into squares.