In a large cast-iron skillet, heat 1 tablespoon of oil. Add apples and cook, cut side down, over moderately low heat, turning once, until golden brown, 7–10 minutes. Transfer to a plate.
Prick sausages with the tip of a small knife. In the skillet, heat remaining tablespoon of oil. Add sausages and cook over moderately high heat, turning occasionally, until browned all over, 3–5 minutes. Arrange apples, cut side up, around sausages and pour wine into the skillet. Bring the liquid to a boil, transfer the skillet to the oven, and roast until the sausages are 160–165°F and the apples are tender, 8–12 minutes.
Remove from the oven and let rest for 5 minutes. Arrange radicchio and arugula on top of the sausages and apples. Spoon some of the pecan vinaigrette over the greens. Garnish with shaved Parmigiano-Reggiano. Sprinkle with flaky sea salt and freshly ground black pepper. Serve immediately.