Warm olive oil in a large skillet over medium heat. (Use a skillet with a lid.) Add garlic and cook for 30-60 seconds, just until fragrant, then stir in the cream, broth, and pesto.
Bring the mixture to a gentle simmer, then stir in the gnocchi. Cover the skillet and cook for 4 minutes, untouched.
Uncover the pan, stir well, and test a gnocchi. Continue to cook, uncovered, stirring frequently, until the gnocchi is tender and the sauce slightly thickened.
When the gnocchi is tender, stir in the Parmesan and lemon juice. Season with salt, pepper, and more lemon juice to taste. (I usually start with 1/4 teaspoon salt and 8-10 cranks of black pepper, but this can vary to taste and depending on how salty your pesto is.)
Garnish with fresh basil, more Parmesan, and lemon zest, if desired, and serve.