Par-cook the gnocchi:

Bring a large kettle of water to a boil. Place the gnocchi in a large skillet and pour boiling water over the top to cover.
Stir in the salt and leave the gnocchi in the water for 30 seconds.
Use a slotted spoon to transfer it to a bowl and gently toss it with the olive oil. Let cool briefly and gently toss again with 3 tablespoons of the pesto.
Scoop out 1/2 cup of the cooking water and discard the remaining water in the pan.
Heat and assemble the rest of the dish:

Set the skillet over medium heat and add the chicken. Cook and stir for about 2 minutes, or until the chicken is warmed through. Add the spinach, and stir for 1 to 2 minutes, or until wilted.
Fold in the cherry tomatoes and 3 tablespoons of the pesto. If the mixture seems dry, stir in 1 to 2 tablespoons of the reserved gnocchi cooking water. Add the gnocchi, and stir very gently until the ingredients are hot.
To serve:

Distribute the goat cheese over the skillet and garnish with parsley or basil if you like.