Bring a large pot of salted water to a boil. Cook penne pasta according to package instructions until al dente. Reserve 1/4 cup of pasta water, then drain.
While the pasta is boiling, season the chicken cubes with salt and pepper.
Heat olive oil in a large skillet over medium-high heat. Add the chicken and cook for 5 to 7 minutes, stirring occasionally, until golden brown and internal temperature reaches 165°F (74°C).
Remove the chicken from the skillet and set aside on a plate.
Reduce the skillet heat to medium. Add the minced garlic and cook for 1 minute until fragrant, taking care not to burn it.
Whisk in the heavy cream, chicken broth, dried oregano, and red pepper flakes. Simmer for 3 to 5 minutes until the sauce begins to thicken slightly.
Reduce heat to low and whisk in the parmesan cheese until melted and the sauce is smooth.
Add the cooked pasta and chicken back into the skillet. Toss to coat evenly, adding a splash of reserved pasta water if the sauce is too thick.
Garnish with chopped fresh parsley and serve immediately.