1. Preheat the oven to 350°F and grease a 9×5-inch loaf pan. Line it with parchment paper for easier removal.

2. In a medium bowl, whisk together the flour, baking powder, and salt.

3. In a large bowl, beat the butter and 1 cup granulated sugar until light and fluffy.

4. Add the eggs one at a time, mixing well after each addition.

5. Mix in the milk, lemon zest, 2 tablespoons lemon juice, and vanilla extract.

6. Add the dry ingredients to the wet ingredients and stir just until combined.

7. In a separate bowl, beat the cream cheese with 1/4 cup granulated sugar and the egg yolk until smooth.

8. Spread half of the batter into the prepared loaf pan.

9. Spoon the cream cheese mixture over the batter, leaving a small border around the edges.

10. Top with the remaining batter and smooth the surface gently.

11. Bake for 50 to 60 minutes, or until the loaf is golden and a toothpick inserted into the bread portion comes out mostly clean.

12. Cool the bread in the pan for 15 minutes, then transfer it to a wire rack to cool completely.

13. Whisk the powdered sugar with 1 to 2 tablespoons lemon juice and drizzle over the cooled loaf before slicing.