Place a large baking pan in the oven. Preheat the oven to 450 degrees F (232 degrees C).

Toss together carrots, Brussels sprouts, onion, olive oil, rosemary, salt, and pepper in a large bowl until combined. Arrange vegetable mixture and sausage in a single layer on the preheated pan.

Bake in the preheated oven until just tender, about 20 minutes. Remove from the oven.

Turn the broiler to high.

Add apple to the pan; broil until apple is tender and vegetables are slightly caramelized, 5 to 6 minutes. Remove from the oven, squeeze lemon over vegetable mixture in the pan, and sprinkle with parsley.