In a large bowl, cream together softened butter and sugar until light and fluffy. Mix in egg and vanilla extract.

In a separate bowl, whisk together flour, baking powder, and salt. Gradually add to wet ingredients, mixing until just combined.

For the filling, beat softened cream cheese and sugar until smooth. Add egg yolk, vanilla extract, and lemon juice (if using), and mix until combined.

Roll spoonfuls of cookie dough into balls and place on a baking sheet. Make an indent in the center of each and fill with cheesecake filling.

Bake at 350°F (175°C) for 12-15 minutes, until edges are lightly golden. Let cool on baking sheet before transferring to a wire rack.

Let cookies cool completely before serving.