Set the oven to 375°F. Line a baking sheet with parchment paper for easy cleanup.
In a small bowl, whisk together 3 tablespoons olive oil, apple cider vinegar, Dijon mustard, sage, salt, and pepper until well combined. Set aside.
Toss the cubed squash with 1 tablespoon olive oil, ½ teaspoon salt, and ¼ teaspoon pepper. Spread it in a single layer on the prepared pan and roast for 20 minutes, or until fork-tender and lightly browned.
Bring a large pot of salted water to a boil. Cook the tortellini according to package directions, drain, and set aside.
Heat 2 tablespoons olive oil in a large skillet over medium heat. Add the shallot and cook for 2–3 minutes, stirring often, until softened. Add the kale and cook for about 3 minutes, or until wilted. Stir in the garlic and cook for 30 seconds. Remove from heat.
Add the cooked tortellini and roasted squash to the skillet. Pour in the dressing and toss gently until everything is evenly coated. Adjust seasoning to taste.
Top with grated Parmesan and serve warm or at room temperature.