Sauté aromatics: Heat olive oil and butter in a large skillet or deep pan over medium heat. Add diced onion and sauté until soft, about 3–4 minutes. Stir in garlic, red pepper flakes, oregano, and basil; cook until fragrant, about 1 minute.
Build the tomato base: Stir in crushed tomatoes and sundried tomatoes (if using). Simmer for 3–4 minutes to deepen the flavor.
Add chickpeas and orzo: Stir in chickpeas and dry orzo. Pour in vegetable broth and stir well. Bring to a gentle simmer, then reduce heat to medium-low.
Cook the orzo: Let the mixture simmer uncovered for 10–12 minutes, stirring occasionally, until the orzo is tender and most of the liquid is absorbed.
Make it creamy: Stir in heavy cream and Parmesan cheese. Mix well until sauce is creamy and orzo is fully coated. Taste and adjust seasoning with salt and black pepper.
Garnish and serve: Remove from heat and top with fresh basil or parsley. Serve hot, with extra Parmesan if desired.