Preheat the oven to 425°F and bring a large pot of salted water to a boil.
Cook the tortellini according to package directions (about 4–5 minutes), drain well, and spread into the bottom of a 9x13-inch baking dish; set aside.
In a small bowl, mix 3 tablespoons olive oil, Italian seasoning, 1 teaspoon salt, and 1/2 teaspoon black pepper to make the chicken seasoning.
Coat the chicken cutlets with the seasoned olive oil, placing them in a shallow dish or zip-top bag to evenly coat.
Grill the chicken over high heat (about 425–450°F) for 7–8 minutes per side, or until an instant-read thermometer registers 165°F; remove and tent with foil to rest.
Meanwhile, make the Alfredo sauce: melt 6 tablespoons butter in a medium saucepan over medium heat, then add 1 tablespoon minced garlic and 1 teaspoon garlic powder and cook briefly until fragrant.
Whisk in 2 tablespoons flour until absorbed, then slowly whisk in 1½ cups whole milk and 1¼ cups heavy cream, bringing the mixture to a gentle boil; reduce heat and simmer 2–3 minutes until slightly thickened.
Remove the sauce from the heat and whisk in 1 cup grated Parmesan until smooth.
Pour the warm Alfredo sauce evenly over the tortellini in the baking dish.
In a small bowl, combine 3 tablespoons seasoned breadcrumbs, 3 tablespoons shredded Asiago, and 1 teaspoon olive oil; sprinkle evenly over the sauced tortellini.
Bake in the preheated oven for about 15 minutes, until the casserole is bubbly and the topping is lightly browned.
Slice the rested grilled chicken and arrange on top of the baked tortellini, then sprinkle with 2 tablespoons chopped fresh parsley and serve immediately.
