Preheat oven to 350° F. Line a large baking sheet with non-stick foil or parchment paper; set aside.
In a large bowl using a hand mixer or stand up mixer, beat butter until light and fluffy. Add powdered sugar and vanilla; beat until combined. Add flour; stir until combined and a soft dough is formed. Shape dough into 1-1/4 inch balls. Roll each ball in crushed almonds. Place each about 2 inches apart on baking sheet. Using thumb or index finger, make an indentation in center of each. Refrigerate 3 to 4 minutes. Bake 12 minutes; remove from oven and set aside to cool.
Meanwhile, in a microwavable bowl, add guava paste and cream. Microwave in 30 second intervals, stirring in between each, until melted and smooth.
Using a teaspoon, carefully press indentation in center again if needed. Fill each center with guava mixture and sprinkle with gorgonzola. Return to oven; bake 5 to 6 minutes longer until cookies are lightly browned.
If guava paste is unavailable in your local supermarket, you can substitute with your favorite preserves or jam.