Prepare the base: In a large deep skillet or pot, heat the butter and olive oil over medium heat. Once melted and slightly hot, add the diced onion, carrots, and celery. Sauté for about 5–7 minutes, stirring occasionally, until the vegetables begin to soften and the onion becomes translucent. Add the minced garlic and cook for another 30–60 seconds until fragrant, being careful not to burn it.

Build the sauce: Sprinkle the flour evenly over the vegetables and stir continuously for 1–2 minutes to cook off the raw flour taste. Slowly pour in the chicken broth while whisking or stirring constantly to avoid lumps. The mixture will begin to thicken slightly as it simmers.

Add cream and seasoning: Stir in the heavy cream, salt, pepper, thyme, parsley, and paprika. Mix well until the sauce becomes smooth and creamy. Allow it to gently simmer for 3–5 minutes so the flavors can combine and the sauce thickens further.

Cook the gnocchi: Add the gnocchi directly into the pot along with the shredded chicken and frozen peas. Stir gently to combine everything, making sure the gnocchi is submerged in the sauce. Cover and let it cook for about 5–8 minutes, stirring occasionally, until the gnocchi is tender and cooked through.

Finish and adjust: Stir in the Parmesan cheese if using, and mix until melted and fully incorporated into the sauce. Taste and adjust seasoning if needed by adding a bit more salt or pepper.

Serve: Remove from heat and let the dish rest for a couple of minutes to thicken slightly. Garnish with fresh parsley if desired, then serve warm directly from the pot for a comforting, creamy chicken pot pie–style meal.