Beat butter in a large bowl until creamy. Gradually add sugar and vanilla, beating well.

Whisk together flour, pineapple, and salt. Gradually add to butter mixture, beating at low speed until combined. Mixture will be crumbly.

Divide dough in half. Press together each half and form into disks. Wrap disks in plastic wrap and chill at least 1 hour.

Allow dough to come to room temperature about 30 minutes prior to rolling (for easier rolling as dough becomes quite hard when chilled).

Heat oven to 275°F. Line baking sheets with parchment paper or non-stick liner.

Roll out dough on a lightly floured surface to 1/4-inch thick.

Cut with 2-inch cutter. Place cookies on baking sheet at least 1-inch apart. Gather and re-roll scraps for more cookies (only once is best).

Refrigerate cut cookies while baking each batch.

Bake for 38 to 40 minutes, until lightly browned on bottom. Transfer cookies to a wire rack and cool completely. Frost cookies and garnish with pineapple.

Beat cream cheese and butter until smooth and combined. Add confectioners sugar and half-and-half. Beat until combined and smooth.

Spread a thin layer of frosting on top of each cookie. Sprinkle top of cookies with pineapple.

Best to sprinkle pineapple on each cookie immediately after spreading frosting before it sets.

Keep cookies chilled when not serving.