Preheat oven to 300-degrees.
Combine the butter and the shredded cheese in a large mixing bowl. Blend the two together on medium speed, about 30 seconds.
Stir in the flour, ½ teaspoon of the kosher salt and the cayenne pepper, blending in on low speed. Check for seasoning, adding the remaining kosher salt if needed.
Turn the dough out onto a sheet of parchment paper that has been lightly dusted with flour.
Shape the dough into a disc, wrap and chill for about 45 minutes.
Place a portion of the dough onto a surface that has been dusted with flour. Keep the remaining dough chilled. Roll the dough to about ⅛” thick, turning the dough as you roll to keep it from sticking to the board.
Cut with a 3” diameter biscuit cutter and place the rounds on a Silpat or parchment lined baking sheet.
Place a date half on one side of each pastry round and gently fold the other half of the dough over the date. Press to seal the edges. The dough is delicate but you can easily press it back together if it tears. If you’re working with large dates you can cut them into smaller pieces.
Bake in a 300-degree oven for about 30 minutes or until the pastry is crisp and golden around the edges.
Let the pastries cool slightly – just enough so you can handle them – then lightly roll them in sugar. If you want a more savory bite you can skip this step.
The pastry dough keeps chilled in the refrigerator for several days. Serve the appetizers warm or at room temperature.