Place whole baby potatoes in a large saucepan and cover with water. Cover with lid and bring to a boil over high heat. Reduce heat to medium and add kosher salt. Simmer until potatoes are tender - about 10 minutes. Drain potatoes and cut into halves or quarters, depending on the size of the potatoes.
Combine lemon olive oil, white balsamic vinegar, Dijon mustard, whole grain mustard and sea salt in a small bowl. Whisk until combined.
In a large bowl toss the potatoes, sliced onion and fresh basil. Pour dressing over and gently toss to coat the potatoes evenly.
Let sit at least 30 minutes to let the flavors meld.