Preheat the oven to 425°F (220°C).
Cook the tortellini in a large pot of salted boiling water according to package instructions (about 4–5 minutes), drain, and transfer to a 9×13 baking dish.
Make the chicken seasoning by whisking 3 tablespoons olive oil, Italian seasoning, 1 teaspoon salt, and 1/2 teaspoon black pepper in a small bowl.
Coat the chicken cutlets with the seasoned oil, then grill over medium-high heat (about 425–450°F) for 7–8 minutes per side, or until an instant-read thermometer reads 165°F (74°C). Remove and tent with foil to rest.
While the chicken rests, make the Alfredo sauce: melt the 6 tablespoons butter in a medium saucepan over medium heat, then add the minced garlic and garlic powder and cook 30 seconds until fragrant.
Sprinkle the flour into the butter mixture and whisk until absorbed, about 1 minute.
Gradually whisk in the whole milk and heavy cream, bring to a gentle boil, then reduce heat and simmer 2–3 minutes until slightly thickened and smooth.
Remove the sauce from heat and whisk in the grated Parmesan until fully incorporated.
Pour the warm Alfredo sauce evenly over the cooked tortellini in the baking dish.
In a small bowl, mix the 3 tablespoons seasoned bread crumbs, 3 tablespoons shredded asiago, and 1 teaspoon olive oil; sprinkle this mixture evenly over the sauced tortellini.
Bake uncovered for about 15 minutes, until bubbly and lightly browned on top.
Slice the rested grilled chicken and arrange it over the baked tortellini, then sprinkle with chopped fresh parsley and serve immediately.