Preheat oven to 350°F (175°C). Grease and lightly flour a standard loaf pan or line it with parchment paper.
In a bowl, whisk together the flour, baking powder, and salt. Set aside.
In a large bowl, beat the softened butter and sugar until light and fluffy. Add the eggs one at a time, mixing well after each addition. Stir in the milk, fresh lemon juice, lemon zest, and vanilla extract. Gradually mix in the dry ingredients until just combined. Do not overmix.
In a separate mixing bowl, beat the softened cream cheese and sugar until perfectly smooth. Add the egg and vanilla extract, mixing until the filling is creamy and free of lumps.
Pour exactly half of the lemon batter into the bottom of the prepared loaf pan. Spoon the cream cheese mixture evenly over the top of it. Finally, top with the remaining lemon batter. Gently swirl the layers together with a butter knife if desired.
Bake in the preheated oven for 50–55 minutes, or until a toothpick inserted into the center comes out mostly clean (a little cream cheese residue on the toothpick is okay, but there should be no wet cake batter).
Let the bread cool in the pan for 15 minutes, then transfer it to a wire rack to cool completely before slicing to ensure the cheesecake center sets properly.
