Bring a large pot of salted water to a boil and cook pasta according to package directions until al dente.
Season chicken cubes with salt, pepper, and dried oregano.
In a large skillet, heat olive oil and butter over medium-high heat.
Add chicken to the skillet and sear until golden brown and the internal temperature reaches 165°F (74°C), approximately 6 to 8 minutes.
Reduce heat to medium, add minced garlic, and sauté for 60 seconds until fragrant.
Pour in heavy cream and simmer for 3 minutes until the sauce begins to reduce slightly.
Incorporate the cooked pasta and grated Parmesan cheese into the skillet.
Toss the mixture continuously, adding reserved pasta water 1 tablespoon at a time until the sauce reaches a glossy consistency that coats the pasta.
Adjust seasoning with additional salt and pepper to taste before serving.