Using a stand mixer fitted with the paddle attachment (or in a large bowl with a handheld mixer), beat 1 cup butter until smooth; about 30 seconds. Scrape down sides of bowl and add ⅓ cup granulated sugar, ⅓ cup light brown sugar and 1 tablespoon lemon zest; beat on medium-high speed until smooth and creamy, about 1 minute.
Scrape down sides of bowl and add 1 egg yolk, 1 tablespoon lemon juice, ¾ teaspoon salt and ½ teaspoon vanilla extract; beat to combine.
Add 2¼ cups flour and 1 tablespoon cornstarch and mix on low until no pockets of dry flour remain. Scrape down sides of bowl and give dough one more mix by hand to ensure no dry flour remains.
Using a tablespoon measure, scoop and roll dough into balls (16g each) and transfer to a parchment-lined baking sheet.
Use your thumb to gently press an indent in center of each dough ball, pressing about three-quarters of the way through; mend any cracked edges.
Return to sheet pan and chill in fridge for at least 30 minutes or up to 2 days. (Indented dough balls can be frozen for up to 3 months.)
Heat oven to 375ºF (190ºC) with rack set in middle position. Line two baking sheets with parchment paper.
Arrange 8 indented dough balls on prepared sheet and fill each with about ½ teaspoon lemon curd.
Bake until edges of cookies are set and just starting to turn golden, about 10 minutes. Remove from oven and let cookies cool on sheet 5 minutes then transfer to a wire rack to cool completely.
Store cookies in an airtight container at room temperature for up to 5 days.