Links of Polish sausage are grilled to highlight their garlicky flavor. Sliced into small pieces, they contrast nicely with buttery Yukon gold potatoes with a light coating of grainy-mustard vinaigrette.
Bring a large pot of water to a boil. Add potatoes and 1 tablespoon salt. Return to a boil; cook until tender, about 8 minutes. Drain; immediately toss with oil, vinegar, mustard, and 1 1/2 teaspoons salt; season with pepper. Refrigerate until cool, about 30 minutes. Stir in chives.
Meanwhile, heat grill to high. Brush grates with oil. Grill kielbasa until heated through and charred, about 3 minutes per side. Cut crosswise on the bias into 2-inch pieces. Serve with potato salad.
Storage: Potato salad can be refrigerated for up to 2 days. Serving Idea: Scoop some sauerkraut alongside the sausage.