Preheat oven to 350°F (175°C). Line a jelly roll pan with parchment paper and lightly grease it.
In a bowl, beat eggs for 3–4 minutes until fluffy. Add sugar and vanilla; beat for 1 minute more.
Sift in flour, baking powder, and salt. Gently fold until just combined. Add milk and fold again.
Pour batter into the prepared pan, spread evenly, and bake for 10–12 minutes until golden and springy.
Turn the cake out onto a clean towel dusted with powdered sugar, peel off parchment, and roll up the cake (with the towel). Let cool.
In another bowl, beat cream cheese and butter until smooth. Add powdered sugar and vanilla. Beat until fluffy.
In a small bowl, mix chopped strawberries with sugar and lemon juice (optional). Let them macerate for 5–10 minutes.
Carefully unroll the cooled cake, spread cheesecake filling evenly, then spoon the strawberries over it.
Gently re-roll the cake, wrap in plastic wrap, and chill for at least 30 minutes.
Slice and serve with whipped cream and fresh berries, if desired.