Grease an 11-inch (25cm) round cake pan and line with parchment paper.
Make the cream cheese filling: In a medium bowl, mix the cream cheese, powdered sugar, and vanilla until fully incorporated and smooth. Set aside.
In a small saucepan over medium heat, cook the strawberry jam until reduced by half, about 20 minutes. Remove the pan from the heat and set aside.
Make the cake batter: In a large bowl, combine the flour, sugar, baking powder, and salt and whisk to combine.
Add the eggs, milk, melted butter, and vanilla and whisk until fully incorporated. Stir in the lemon zest and juice.
Pour the batter into the prepared cake pan.
Preheat the oven to 350˚F (180˚C).
Transfer the reserved cream cheese filling and reduced jam to 2 piping bags fitted with round tips or zip-top bags with a corner cut off.
Starting in the center, pipe in a layer of jam in a spiral shape, moving towards the outside of the cake. Pipe a layer of cream cheese filling on top of the jam, following the swirl as closely as possible.
Bake for 30 minutes, until a toothpick inserted in the center of the cake comes out clean. Allow cake to come to room temperature before removing from cake pan.
Make the lemon glaze: combine the powdered sugar, lemon zest, and lemon juice in a medium bowl and whisk until a smooth glaze forms.
Remove the cooled cake from the pan and evenly pour over the glaze.