Preheat the oven to 425°F (218°C).
Cook the tortellini according to package directions (about 4–5 minutes), drain well, and transfer to the bottom of a 9×13-inch baking dish; set aside.
In a small bowl, whisk together 3 tablespoons olive oil, Italian seasoning, 1 teaspoon salt, and 1/2 teaspoon black pepper to make a seasoning oil for the chicken.
Place the chicken cutlets in a shallow dish or a zip-top bag and coat evenly with the seasoned olive oil.
Grill the chicken over high heat (about 425–450°F or medium-high) for 7–8 minutes per side, or until the internal temperature reaches 165°F (74°C). Remove from the grill and tent with foil to rest while you make the sauce.
In a medium saucepan over medium heat, melt the butter. Add the minced garlic and garlic powder and cook briefly until fragrant, about 30 seconds.
Sprinkle the flour into the butter mixture and whisk until fully absorbed and smooth.
Slowly whisk in the whole milk and heavy cream, smoothing out any lumps. Bring the sauce to a gentle boil, then reduce heat and simmer 2–3 minutes until slightly thickened.
Stir in the grated Parmesan until melted and incorporated, then remove the Alfredo sauce from the heat.
Pour the warm Alfredo sauce evenly over the tortellini in the baking dish.
In a small bowl, combine the seasoned breadcrumbs, shredded asiago, and 1 teaspoon olive oil; sprinkle this mixture evenly over the sauced tortellini.
Bake for about 15 minutes, until the sauce is bubbly and the topping is lightly browned.
While the casserole bakes, slice the rested grilled chicken into pieces.
Top the baked asiago tortellini Alfredo with the sliced grilled chicken and sprinkle with chopped fresh parsley before serving.