Preheat the Oven & Prepare the Pan:
Preheat your oven to 325°F (165°C). Grease and lightly flour a loaf pan or line it with parchment paper for easy removal.
Make the Pound Cake Batter:
In a medium bowl, whisk together the flour, baking powder, and salt. Set aside. In a separate large bowl, cream together the softened butter and sugar until light and fluffy. Add the eggs one at a time, mixing well after each addition. Stir in the vanilla extract. Gradually add the dry flour mixture, alternating with the milk, until everything is well combined and smooth.
Prepare the Cheesecake Layer:
In a small bowl, beat the softened cream cheese with 1/4 cup of sugar until smooth. Add the egg and vanilla extract, and mix until fully incorporated.
Make the Strawberry Swirl:
In a small saucepan, combine the pureed strawberries and sugar. Heat over medium heat, stirring occasionally, for about 5-10 minutes, or until the mixture thickens slightly. If you prefer a thicker swirl, stir in the cornstarch and let the mixture simmer for another 2 minutes. Remove from heat and let it cool slightly.
Layer the Batter:
Pour half of the pound cake batter into the prepared pan. Gently spread the cheesecake mixture over the cake batter. Spoon the strawberry swirl across the cheesecake layer, then top with the remaining pound cake batter. Use a knife to gently swirl the strawberry mixture into the batter for a marbled effect.
Bake the Cake:
Bake in the preheated oven for 60-75 minutes, or until a toothpick inserted into the center comes out clean. If the top starts to brown too quickly, tent the cake with foil and continue baking.
Cool and Serve:
Let the cake cool completely in the pan before removing it. Once cooled, slice and serve. The cake can be enjoyed at room temperature or chilled for a denser texture.