Preheat oven to 350 F. Line a 2 baking sheets with parchment paper.
In a medium bowl, whisk together flour, baking powder, cinnamon & salt.
In a large bowl, cream together butter & sugar with a mixer until light. Beat in lime zest & egg followed by lime juice & rum. Gradually beat in the flour mixture, scraping down the sides of the bowl as you work, until it comes together.
Divide dough into three portions, wrapping 2 in plastic wrap & place in refrigerator while you are working on the first piece.
Place the first piece on a lightly floured surface & roll out to 1/3-inch thickness. Using a lightly floured 2-inch round cookie cutter, cut out circles of the dough. Place on baking sheet. Repeat with remaining dough.
Cut pieces of guava paste into dime-sized circles or squares ( depending on what shape your guava paste comes in), making each approximately 1/4-inch thick. Lightly press one piece into the top of each cookie.
Bake for 13-16 minutes, until cookies are light gold at the edges. Cool on the baking sheet for 4-5 minutes, then transfer to a wire rack to cool. If you wish you can dust the cookies with powdered sugar.
Recipe Notes
As an alternate idea, assemble them similar to a ‘linzer’ cookie. Roll half of the dough to 1/8-inch thickness; cut with a circular (more decorative) cookie cutter. Repeat with remaining dough but cut small circles in the center of these.
On top of each plain cookie, place one with a hole in it. Press a guava ‘circle’ in the hole & sprinkle with a few chopped pistachios if you wish.
I used this method for the blog picture. Same cookie just a bit fancier.