In a large pot of boiling salted water, add the gnocchi and cook according to package instructions, typically until they float (about 2-3 minutes). Drain and set aside.
In a large skillet over medium heat, add olive oil. Once hot, add the diced chicken. Season with garlic powder, onion powder, salt, and pepper. Cook for 6-8 minutes until the chicken is cooked through and golden brown.
Add the cooked gnocchi to the skillet with the chicken. Pour in the heavy cream and pesto sauce, stirring well to combine all the ingredients.
Fold in the halved cherry tomatoes, cooking for an additional 2-3 minutes until the tomatoes soften slightly.
Remove from heat and stir in the grated Parmesan cheese until well blended. Adjust seasoning if necessary.
Serve hot, garnished with fresh basil leaves on top.