Combine pesto with ¼ cup of oil and set aside.
Heat oil in a large skillet over low heat. Add the Gnocchi and stir occasionally to coat in the oil and allow them to brown slightly, about 4-6 minutes. Be careful not to burn the gnocchi. Increase heat to medium and add the pesto mixture and stock. Continue cooking until gnocchi has been coated and most of the liquid has evaporated, about 8-10 minutes.
Divide among 6-8 bowls and finish with shredded cheese and black pepper as desired.