In a large skillet, heat olive oil and butter over medium heat until melted, about 1-2 minutes. Add chopped onion and minced garlic, sautéing for approximately 3 minutes until onion turns translucent and fragrant.

Stir in the orzo and continue to cook for about 2 minutes, allowing it to lightly toast.

Pour in the chicken broth and bring the mixture to a gentle simmer, uncovered. Cook for about 10 minutes, stirring occasionally, until the orzo is al dente.

Reduce the heat to low, then slowly stir in the heavy cream and grated Parmesan cheese. Mix until the sauce is smooth and creamy, about 1-2 minutes.

Gently fold in the shrimp, ensuring they are evenly distributed throughout the skillet. Cook for 3-4 minutes, stirring occasionally, until the shrimp turn pink and opaque.

Season the dish with salt and black pepper to taste, then remove the skillet from heat and sprinkle with fresh parsley.