Boil potatoes and garlic in a large pot of salted water until just tender, 15 to 20 minutes. Drain and let cool to room temperature. Discard the garlic.
Whisk mayonnaise, vinegar, olive oil, and sambal oelek together in a large bowl. Season with salt and pepper to taste.
Roughly chop cooled potatoes into a large bowl. Add cornichons, mustard greens, and mayonnaise mixture. Toss to coat. Cover and set aside in the refrigerator for 1 hour. Season with salt and pepper to taste.