Preheat the oven to 400˚Line a large sheet pan with parchment paper or foil and set aside.
Prep the veggies:
Peel and thinly slice the carrots. Halve the zucchini and cut thick coins of the zucchini. Coarsely chop the broccoli. Remove the stems and seeds from the peppers and chop into medium-sized pieces. Chop the sausage into thick coins.
Pour the veggies and sausage onto a sheet pan.
Mix remaining ingredients except parsley and Parmesan and coat the veggies and sausage generously with the oil mixture. Bake until the veggies are tender.
Sprinkle with finely grated Parmesan and fresh parsley to serve.