One Skillet Gnocchi with Brussels Sprouts and Chickpeas

extra virgin olive oil (, divided)

butter

package ((12 ounces) gluten-free, wheat-free gnocchi)

large yellow onion (, thinly sliced)

garlic (, minced)

bag ((12 ounces) frozen small brussels sprouts)

low sodium vegetable broth

((15-ounces) no-salt added diced tomatoes)

((15-ounces) chickpeas, well rinsed and drained)

salt and fresh ground pepper (, to taste)

shredded mozzarella cheese

shredded Parmesan cheese