In a large pot of boiling salted water, cook gnocchi, stirring occasionally, until just al dente and floating, 1 to 2 minutes. Using a slotted spoon, transfer to a paper towel-lined baking sheet.
In a large skillet over medium-high heat, heat 1 tablespoon oil. Cook pancetta, stirring occasionally, until crispy and fat has rendered, 3 to 4 minutes. Using a slotted spoon, transfer to a plate, leaving fat in skillet.
In same skillet over medium-high heat, cook gnocchi, tossing in fat occasionally, until lightly golden and crisp, 3 to 4 minutes. Let cool slightly.
In a large bowl, whisk garlic, vinegar, basil, oregano, 1 teaspoon salt, and remaining 3 tablespoons oil. Add gnocchi, olives, ciliegine, artichokes, pepperoni, salami, and tomatoes. Sprinkle with pancetta.
