Heat olive oil and butter in a large skillet over medium heat. Add the diced chicken and season with salt and pepper. Cook until golden and cooked through, about 5–6 minutes. Remove chicken from the skillet and set aside.
In the same skillet, add the diced onion and cook for 2–3 minutes until softened. Add the garlic and cook for another 30 seconds until fragrant.
Pour in the chicken broth and heavy cream, stirring to combine. Add the gnocchi, thyme, and bring to a gentle simmer. Cook for 5–6 minutes, stirring occasionally, until the gnocchi is tender and the sauce begins to thicken.
Return the cooked chicken to the skillet. Stir in Parmesan cheese until melted and incorporated into the sauce.
If using spinach, stir it in during the last minute of cooking until wilted. Taste and adjust seasoning. Garnish with fresh parsley and serve warm.