Preheat the grill or grill pan to medium-high heat. Season the chicken breasts with olive oil, salt, and pepper.
Grill the chicken for 6-7 minutes on each side or until fully cooked and juices run clear. Remove from the grill and let it rest for 5 minutes before slicing.
In a large pot, bring salted water to a boil. Add the Asiago tortellini and cook according to package instructions, usually 3-5 minutes. Drain and set aside.
In a skillet over medium heat, add olive oil and sauté minced garlic until fragrant, about 1 minute.
Pour in the heavy cream and bring to a gentle simmer. Reduce heat to low, then gradually whisk in the grated Asiago cheese until melted and the sauce is creamy. Season with salt and pepper to taste.
Add the cooked tortellini to the sauce in the skillet and toss to combine, ensuring the tortellini is well coated.
Slice the grilled chicken and serve over the creamy tortellini. Garnish with fresh parsley and additional Parmesan cheese if desired.