Preheat the oven to 425 degrees F and line 2 baking sheets with parchment paper. Cut the kielbasa sausage into 16 equal pieces. Unwrap and cut the American cheese slices in half, creating 16 strips. Use a coarse grater to shave the jalapeño into fine pieces.
Press one roll flat into a 4 1/2-inch circle. Sprinkle a scant amount of shaved jalapeño over the dough. Place a cheese strip over the jalapeños, then a sausage link on top.
Fold the ends of the dough over the sausage link, covering the cheese completely, so it's less likely to seep out. Press the seam to secure the dough. Then flip the roll over, placing it seam-side-down on a baking sheet. Repeat with the remaining ingredients creating 16 sausage rolls. Spread them out on the baking sheets.
Brush each roll thoroughly with milk. If desired, sprinkle with flake or coarse salt. Bake for 10-15 minutes, until golden. Cool for 5 minutes, then serve warm.