Preheat oven to 350°F. Line a baking sheet with parchment paper.
Cut the butter into small pieces and add it to a bowl with the flour and salt. Using your hands, quickly knead the ingredients until a crumbly dough forms.
Wash and chop the basil.
Add the grated cheddar, chili, and basil to the dough crumbs and mix well.
Add a little cold water if the dough is too dry. Then quickly knead the dough together and shape it into a ball. Wrap the dough in plastic wrap and place it in the refrigerator for an hour.
Roll out the dough on a floured surface until it's about ¼ inch thick.
Use a cookie cutter to cut out round shapes from the dough and place them on the prepared baking sheet.
Whisk the egg yolk and brush it over the surface of the cookies.
Bake the cookies for about 15 minutes, until lightly browned, and let them cool completely before serving.