Heat an outdoor grill to medium-high heat. Prepare 4 (8x8-inch) sheets of heavy-duty aluminum foil and set aside.

Place the sausages, baby potatoes (or brussel sprouts), and green beans in a large bowl. Add the Cajun seasoning and butter and toss to coat everything in the spicy, buttery goodness.

Divide the potato (or brussel sprouts) and green bean mixture between the 4 pieces of foil. Fold each piece of foil up into a tight packet that is completely sealed — fold 2 opposing sides together and then crimp the edges closed.

Place the packets on the grill. Cover and grill until the potatoes (or brussel sprouts) are tender, about 25 minutes. Use caution when opening the packets, as they are quite steamy.