Season chicken with salt, pepper, and Italian seasoning.
Heat olive oil and butter in a large skillet over medium-high heat. Add chicken and cook until golden and cooked through. Remove and set aside.
Reduce heat to medium. Add garlic to the skillet and cook until fragrant, about 30 seconds.
Pour in chicken broth, scraping up any browned bits from the pan. Stir in cream and bring to a gentle simmer.
Add gnocchi directly to the skillet. Simmer, stirring occasionally, until gnocchi are tender and sauce thickens.
Stir in Parmesan cheese until melted and smooth.
Return chicken to the skillet and toss to coat evenly.
Taste and adjust seasoning. Garnish and serve hot.