Preheat oven to 350°F (175°C). Line a rimmed baking sheet with parchment and grease lightly. Whisk eggs and sugar until pale, add vanilla and butter, fold in flour and salt. Spread thinly on the sheet and bake 8–10 minutes. Cool slightly, flip onto parchment, peel, and trim to a neat rectangle.

Beat cream cheese and sugar until smooth, add vanilla and lemon. Whip cold heavy cream to soft peaks and fold into cream cheese mixture until light and spreadable.

Lay cake sheet on plastic wrap or mat. Spread an even layer of cheesecake filling leaving a small border. Add thin lines of warm jam and arrange strawberry slices. Roll tightly with help of mat/plastic wrap, seal seam, and wrap tightly. Refrigerate 2–4 hours.

Unwrap the chilled log. Using a hot, clean knife, slice into 1-inch rounds. Arrange on a platter, dust with powdered sugar, garnish with mint and extra berries, and serve chilled.