Preheat the oven to 425°F. Cut the Yukon Gold potatoes into roughly 1-inch cubes. You can peel them if you prefer, but I like to leave the skins on for extra texture.
Place the potatoes on a baking sheet and toss them with enough olive oil to lightly coat. Season with salt and pepper. Spread them into an even layer and roast for 30–40 minutes, or until fork-tender and lightly golden around the edges.
Remove the potatoes from the oven and allow them to cool completely before adding the dressing. This helps keep the dressing creamy instead of becoming oily or runny from the heat.
In a large bowl, stir together the mayonnaise, sweet relish, yellow mustard, sugar and ½ tablespoon of vinegar. Taste and add additional vinegar if you prefer a tangier potato salad.
Add the cooled roasted potatoes and sliced green onions to the bowl. Gently toss until the potatoes are evenly coated in the dressing. Taste and season with additional salt and pepper as needed.
Cover and refrigerate the potato salad for at least 2 hours before serving. This gives the flavors time to blend together. Serve chilled and enjoy!