Step 1: Preheat your oven to 375°F (190°C). Line a 15x10 inch baking pan with parchment paper, leaving an overhang on the long sides.
Step 2: In a big bowl, whisk together the eggs and sugar until pale, thick, and ribbons form when lifting the whisk. Stir in the vanilla extract.
Step 3: In a separate, smaller bowl, whisk together the flour, baking powder, and pinch of salt.
Step 4: Gently fold the dry ingredients into the egg mixture using a spatula until just combined. Do not overmix.
Step 5: Pour the batter into the prepared pan and spread evenly into the corners.
Step 6: Bake for 12 to 15 minutes, or until the cake springs back gently and a toothpick comes out clean.
Step 7: Immediately lay a clean kitchen towel flat and dust generously with powdered sugar. Invert the hot cake onto the sugared towel and carefully peel off the parchment paper.
Step 8: While the cake is still hot, roll it up from one of the short ends using the towel to help. Let the rolled cake sit seam-side down on a wire rack and cool completely.
Step 9: While the cake cools, make the filling. In a large bowl, beat the softened cream cheese with sugar until super smooth and creamy. Beat in the vanilla extract.
Step 10: In a separate bowl, whip the cold heavy cream until stiff peaks form.
Step 11: Gently fold the whipped cream into the cream cheese mixture until just combined.
Step 12: For the compote, combine sliced strawberries, sugar, and lemon juice in a medium saucepan.
Step 13: Cook over medium heat for 5 to 7 minutes, stirring occasionally, until the strawberries soften and release juices. Mash some berries if desired. Let cool completely.
Step 14: For the crumble, combine crushed Oreos, cold butter cubes, and sliced strawberries in a medium bowl. Use fingers or a pastry blender to mix until crumbly.
Step 15: Once the cake is completely cool, gently unroll it from the towel.
Step 16: Spread the cheesecake filling evenly over the cake, leaving about a half-inch border on one short end.
Step 17: Spoon and spread the cooled strawberry compote over the cheesecake filling, distributing chunks evenly.
Step 18: Starting from the filled short end, tightly roll the cake back up slowly and evenly.
Step 19: Place the roll seam-side down on a platter or parchment paper. Sprinkle the Oreo-strawberry crumble over the top.
Step 20: Refrigerate the roll for at least 2 hours to allow the filling to firm up and the roll to hold its shape. Best served after chilling overnight.