Preheat the oven to 350 degrees F with the racks in the upper and lower thirds of the oven. Line 2 sheet pans with parchment paper and set aside.
Add the cheese, flour, butter, salt and BBQ mix to the bowl of a food processor and pulse until the mixture resembles coarse meal. Add the cream and pulse until a ball forms.
On a lightly floured work surface, roll the dough out to 1/4 to 1/8-inch thick. Cut the dough with a sharp knife into 1/4-inch wide strips. Transfer to the prepared sheet pans, leaving space between them, and bake until golden brown, about 15 minutes. Flip the pans once halfway through the cooking time. Cool completely on the sheet pans.
BYOC: If your friends are the spicy type, try adding a pinch or 2 of cayenne. If you want to get the kids involved, omit the BBQ spice, have them paint the straws with egg wash before you bake them and add some sesame seeds or poppy seeds.