Place a large skillet over medium-high heat with the butter and EVOO. Once the butter has melted, add the onions and garlic and cook, stirring frequently, for about 20 minutes, until brown and caramelized. If the edges start to get too much color, just add a little water and stir it up.
While the onions and garlic are cooking, bring a large pot of water to a boil over high heat to cook the gnocchi. Once boiling, add some salt and the gnocchi, and cook according to package directions. Remove 1/4 cup of starchy cooking liquid before draining the gnocchi and add it to the pan of onions.