Preheat oven to 350°
Beat Cheddar cheese, butter, half-and-half, and salt at medium speed with a mixer until blended. Gradually add flour, Parmesan cheese, and basil – beating just until combined.
Turn dough onto a well floured surface. Divide into 3 equal portions, and roll to flatten each to ⅛ inch thickness. Cut with star shaped cutter. Place 1 inch apart on parchment paper-lined baking sheets.
Bake 11 to 14 minutes or until golden; cool on baking sheets on wire racks for 30 minutes.