Bring a large pot of salted water to a boil and cook tortellini according to package instructions until al dente. Drain and set aside.
Season the cubed chicken with salt and black pepper.
Heat olive oil in a large skillet over medium-high heat. Add the chicken and cook until golden brown and internal temperature reaches 165 degrees Fahrenheit, approximately 5 to 7 minutes.
Remove the chicken from the skillet and set aside on a plate.
In the same skillet, reduce heat to medium and add minced garlic. Sauté for 1 minute until fragrant, being careful not to burn.
Stir in the heavy cream, chicken broth, and dried oregano. Bring to a gentle simmer.
Whisk in the Parmesan cheese and continue to simmer for 2 to 3 minutes until the sauce begins to thicken.
Add the baby spinach to the sauce and stir until just wilted.
Return the cooked chicken and drained tortellini to the skillet. Toss thoroughly to ensure even coating in the sauce.
Garnish with fresh parsley and serve immediately.