Combine butter and sugars in the bowl of a stand mixer and beat until well-creamed.

With mixer on low, stir in egg yolk and vanilla extract, pausing to scrape down the sides and mixing until well-combined.

In a separate bowl, whisk together flour, graham cracker crumbs, cornstarch, and salt.

Gradually add the flour mixture to your wet ingredients, ensuring all ingredients are well-combined.

Scoop cookie dough into 2-teaspoon-sized balls and roll until smooth.

Use your thumb to gently press an indent in the center of each cookie dough ball.

Chill imprinted dough in freezer for 30 minutes.

Preheat oven to 350F (175C) and line cookie sheets with parchment paper.

Place chilled cookie dough on sheet spacing at least 1" apart.

Bake on 350F (175C) for 10-11 minutes and allow to cool completely on pan.

In a small saucepan over medium-low heat, combine white chocolate chips, condensed milk, and key lime juice.

Stir frequently until chocolate is melted and ingredients are well-combined. Stir in lime zest until mixture just begins to bubble.

Reduce heat to low and spoon filling into thumbprints of cookies.

Allow to cool completely before serving.