Drain the canned chicken thoroughly and break it apart into bite-sized pieces in a large mixing bowl. Finely mince the onion into small 1/8-inch pieces to distribute its flavor evenly throughout the salad. Dice the celery into similar small pieces, then halve the grapes lengthwise. Add the mayonnaise and Dijon mustard to the chicken, then fold in the celery, onion, grapes, and slivered almonds until everything is evenly combined. Set the chicken salad aside while you prepare the crescent roll shells.

Preheat your oven to 375°F. Crumple foil into balls roughly the size of a golf ball—these will create the hollow centers for your carrot-shaped rolls. Unroll the crescent roll dough and separate it into individual triangles. Wrap 2 crescent triangles around each foil ball, stretching and overlapping them slightly to form a carrot or egg shape, then place them seam-side down on a baking sheet. Bake for 12-15 minutes until the rolls are golden brown and crispy.

Remove the baking sheet from the oven and let the rolls cool for a few minutes until they're safe to handle. Carefully remove the foil balls from the center of each roll—they should slide out easily. Once the rolls have cooled to room temperature, spoon the chicken salad mixture generously into the hollow centers of each crescent roll.

Finely chop the fresh parsley and sprinkle it over the top of each filled roll as a fresh, festive garnish. Arrange the chicken salad crescent rolls on a serving platter and serve immediately while the rolls are still slightly warm and crispy.