Preheat oven to 350°F. Lightly spray a standard 12-cup muffin tin with nonstick cooking spray. Set aside.
On a lightly floured work surface, roll out each tube of dough to a 12×16-inch rectangle. If using perforated crescent roll dough, pinch the seams to seal.
In a medium bowl, combine softened butter, chives, and garlic.
Spread about ⅓ of the butter mixture over one sheet of dough.
Evenly sprinkle 1 cup of cheddar cheese over the butter mixture.
Starting on the long end of the dough sheet, roll it tightly into a log.
Cut the log in half, creating two shorter logs, and then cut each of those logs in half lengthwise, giving you four sections of dough.
Repeat with the remaining two sheets of dough until you have 12 sections.
Roll each section tightly into a cinnamon roll shape, with the layered side facing out. Tuck in the end piece of dough.
Place each roll into the prepared muffin tin.
Bake for 20-25 minutes, or until golden brown. While the cruffins are baking, prepare the garlic butter.
In a small bowl, whisk together melted butter, garlic, chives, and salt.
Brush the garlic butter over the warm cruffins immediately after removing them from the oven.