Preheat your oven to 350°F (175°C) and prepare your baking sheets by lining them with parchment paper.

In a mixing bowl, combine the shredded cheddar cheese, softened butter, half-and-half, and kosher salt. Beat these ingredients together until creamy, about 2-3 minutes.

Gradually add the all-purpose flour, grated Parmesan cheese, and finely chopped basil to the creamy mixture. Fold together gently until just combined.

Transfer the dough to a floured surface, divide it into three portions, and roll each out to about ⅛ inch thickness. Cut into desired shapes.

Place the cut dough an inch apart on the baking sheets and bake for 11 to 14 minutes until golden brown.

Remove from the oven and allow to cool on wire racks for approximately 30 minutes before serving.