In a large mixing bowl, toss potatoes with 2-3 tablespoons olive oil, 1 teaspoon salt, and half of the ground pepper.

When the oven is at temperature, remove the sheet pan and spread the potatoes out onto the hot pan, arranging them with the cut sides facing down. Set the mixing bowl aside.

Nestle the sausage links on the pan among the potatoes. Using a pastry brush, brush the links with some of the olive oil leftover in the mixing bowl.

Transfer sheet pan to oven with oven mitts (it might still be hot!) and roast 30 minutes, tossing halfway through cooking time.

While the potatoes and the sausages cook, place the broccolini in the reserved mixing bowl and toss to coat, adding additional 1 tablespoon olive oil, remaining ½ teaspoon salt and pepper as needed.

At 30 minutes, remove sheet pan from the oven and add chicken stock and scatter the garlic over everything. Toss the sausage and potatoes to coat then nestle the broccolini on top. Transfer back to the oven and cook another 8-10 minutes, until the broccolini starts to get brown on the edges. Remove from oven and serve.