Beat ½ cup softened butter with ½ cup powdered sugar until light and fluffy, about 3-4 minutes. Add 1 egg yolk, ½ teaspoon lime zest, and 1 teaspoon vanilla and beat until well combined. Scrape the bowl and add 1 ½ cups all-purpose flour, ¾ cup superfine almond flour, and ¼ teaspoon salt. Mix until just combined. Shape the cookie dough into a flattened disc, wrap in plastic wrap, and chill for 1 hour.
Dust a clean work counter with flour and remove the cookie dough from the fridge. Roll out the dough until it's about ⅛ inch thick and cut out 2 ½ inch round circles. Lay the cut cookies on a lined baking sheet and chill in the freezer.
Preheat oven to 350 degrees.
Remove the cookies from the freezer when they are firm, about 10 minutes. Using the smallest cutter, cut out the center of half of the cookies. Bake the cookies for 8-10 minutes, rotating the baking sheet halfway through. Remove cookies from the oven and let them cool on the baking sheet for 2 minutes before transferring them to a wire rack to cool completely.
Spread about 1 tablespoon kaya jam on the bottoms of the cookies. Top with a cookie with the center cut out. Dust with powdered sugar and serve.