In a large skillet, heat the olive oil over medium heat. Add the diced onion and sauté for about 5 minutes, until translucent. Stir in the minced garlic and cook for an additional 1 minute until fragrant.
Pour in the diced tomatoes (with juices) and bring to a simmer. Cook for about 5 minutes, allowing the flavors to meld.
Reduce the heat to low and stir in the heavy cream, dried basil, and dried oregano. Season with salt and pepper to taste. Let the sauce simmer gently while you cook the gnocchi.
In a separate pot, bring salted water to a boil. Add the potato gnocchi and cook according to package instructions, usually about 2-3 minutes or until they float to the surface. Drain the gnocchi.
Add the cooked gnocchi to the creamy tomato sauce, gently stirring to coat the gnocchi evenly.
Tear the burrata cheese into pieces and gently fold it into the gnocchi and sauce. Allow it to warm through for about 2 minutes.
Serve immediately, garnished with fresh basil leaves and grated Parmesan cheese.