Preheat the oven to 375°F (190°C) for about 10 minutes, or until fully heated. Line a 13 x 18-inch (33 x 46 cm) rimmed baking sheet with parchment paper.

Unroll the cold crescent dough and separate it along the perforations into 8 triangles. Work for about 2 minutes at room temperature, keeping the dough cool and intact without stretching it excessively.

Sprinkle 1 tablespoon (7 g) of cheddar cheese over the wide end of each dough triangle, then place one fully cooked sausage link over the cheese. Assemble for about 3 minutes at room temperature, keeping the filling near the wide end so the dough rolls neatly.

Starting at the wide end, roll each triangle around the sausage toward the pointed tip, taking about 2 minutes total. Place the rolls tip-side down on the prepared baking sheet with about 2 inches (5 cm) between them; they should look snugly wrapped without torn dough.

Brush the tops evenly with the melted butter at room temperature for about 1 minute. The surface should have a thin, even coating rather than pools of butter around the rolls.

Bake at 375°F (190°C) for 11 to 13 minutes, or until the crescent dough is puffed and evenly golden brown and the cheese is melted. Let the rolls stand on the baking sheet for 2 minutes before serving so the hot filling can settle.