Place the slivered almonds in a food processor and add 1/4 cup sugar. Grind almonds finely. Beat the butter and remaining 3/4 cup sugar until well blended. Beat in the egg yolk, vanilla extract and salt. Add the ground nut mixture and flour and beat until moist clumps form. Mound into 2 balls and flatten each ball into a disc. Wrap in plastic and refrigerate for at least 30 minutes and up to 2 days.
Preheat oven to 325 degrees F.
Line 2 baking sheets with parchment paper. Roll out half of the dough between the two sheets of parchment paper to 1/4-inch thickness, sprinkling with flour on both sides of the dough and rotating as you roll so it doesn't stick to the paper. Place the dough still in the parchment paper on a baking sheet and refrigerate for 10 minutes. Use a 2-inch round cookie cutter or biscuit cutter to to cut out cookies. Peel away the the extra dough from the cookie rounds and gently rearrange the cookies on the parchment to space them 1/2 inch apart. If the cookies start to stretch, refrigerate for another 5-10 minutes until they're firm enough to move.
Chill cookies for 10 minutes before baking.
Gather scraps and reroll the dough using the same technique as before, in between two pieces of parchment and refrigerate for 10 minutes and cut out more cookies.
Bake cookies for 10-11 minutes in the middle rack of the oven or until the cookies begin stop bubbling but are still light in color.
Cool for 5 minutes on the baking sheet then transfer to a rack to cool completely. Repeat with remaining dough.
For the White Chocolate and Semi Sweet fillings:
Divide the cream between two separate sauce pans. Bring to a simmer and remove from the heat. Add the white chocolate to one pan and whisk until smooth. Add the semi sweet chocolate chips to the other saucepan and whisk until smooth. Pour the mixtures into ramekins or small bowls and let cool for about two hours.
Place half of the cookies, bottom side up on a work surface. Spread the white chocolate ganache filling on half of the bottom side up cookies and the semi sweet chocolate ganache on the other half. Top each with a second, plain cookie bottom side down, pressing lightly to join the cookies.
Melt the semi sweet chocolate and the white chocolate in individual ramekins at 30 second increments, stirring between each burst of microwaving. When the chocolate starts to melt, reduce the microwave bursts to 15 seconds. Don't heat for too long without stirring or the chocolate will seize and become a big clump of unusable chocolate.
Dip the end of a cookie in the semi sweet chocolate or spread evenly with a knife. Sprinkle with the toasted almond bits. Alternately, dip the cookie in the white chocolate or spread evenly with a knife and sprinkle with the peppermint baking chips.
Transfer to a cooling rack and allow the chocolate until set and repeat with remaining cookies.
Very slightly adapted from Bon Appetit
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