Cook gnocchi according to the package instructions; drain and set aside.
Heat the olive oil in a large, deep skillet over medium heat. Season the chicken with salt, garlic powder, and smoked paprika, then place smooth side down into the warm skillet. Pan-sear the chicken for 4-5 minutes per side, then transfer to a plate.
Add a splash of broth to the skillet to scrape up any brown bits, then add onion and sauté for 3-4 minutes. Add the butter and allow it to melt, then add tomatoes, garlic, and a pinch of salt, cooking for 3 minutes.
Add spinach and stir until wilted.
Pour the remaining broth into a measuring cup along with cream and flour; whisk to combine. Pour the sauce into the skillet and bring it to a low simmer. Slowly stir in parmesan cheese until smooth, then simmer for 2 minutes to thicken.
Add in the cooked gnocchi and stir to coat in the sauce. Nestle the chicken back into the skillet and simmer for 1-2 minutes. Garnish with salt, pepper, and extra cheese before serving.