Heat the olive oil in your large skillet over medium heat. Once shimmering, add the chopped onion and cook until softened and translucent, about 5 minutes. Stir in the minced garlic and cook for another 30 seconds until fragrant, taking care not to let it burn.
Stir in the drained diced tomatoes and dried basil. Let this simmer with the aromatics for 3-4 minutes, allowing the tomatoes to meld with the onion and garlic. Season with salt and pepper to taste.
Lower the heat and pour in the heavy cream. Stir well to combine and bring the sauce to a gentle simmer. Let it thicken slightly, about 3 minutes, stirring occasionally.
Add the gnocchi directly into the skillet with the sauce, gently folding them in to coat each piece. Cook for 5-6 minutes, stirring occasionally, until the gnocchi are tender and cooked through. If adding cooked chicken or turkey, stir it in now to warm through.
Turn off the heat and stir in the chopped fresh basil leaves and grated Parmesan cheese. The residual heat will melt the cheese and release the basil’s aroma, creating a creamy, flavorful finish.
Spoon your beautiful Creamy Tomato-Basil Gnocchi Skillet into bowls or onto plates. Garnish with whole basil leaves or extra Parmesan if desired. Serve immediately for best flavor and texture.