Preheat a large grill pan or skillet over medium heat. Add sausage and cook 12 to 15 minutes, turning to brown on all sides. In a bowl, toss onion rings in 1 tablespoon olive oil, then add to the pan with the sausages. Cook until nicely browned, about 10 minutes. Remove.
Heat 3 tablespoons olive oil in a separate heavy skillet over medium heat. Add garlic and brown 30 seconds. Add spinach and stir with a wooden spoon until wilted, about 2 to 3 minutes. Remove from heat and press excess liquid from spinach. Remove spinach to a bowl, then toss with salt and pepper; keep warm. In the same skillet, heat 3 more tablespoons oil over medium-low heat. Add 2 tablespoons apple cider vinegar and 1 tablespoon mustard. Add apples and cook until they soften slightly, about 5 to 6 minutes. Remove apples to a plate; keep warm. In the skillet, whisk together the remaining 2 tablespoons vinegar and 1 tablespoon mustard until slightly emulsified, adding more salt and pepper to taste. Set dressing aside.
To assemble sandwiches, split rolls from the top. Drizzle dressing on each roll. Divide wilted spinach among the rolls. Place sausage on spinach, layer with apples, and top with onion. Serve immediately.