1. Place potatoes in a large pot and add enough water to cover; generously salt water and add bay leaf. Bring to a boil over high heat and cook until potatoes are easily pierced with the tines of a fork, 15 to 20 minutes. Slice crosswise into 1-inch-thick rounds.

2. Preheat a grill: If using a charcoal grill, make a fire in your grill. When the charcoals are completely covered in gray ash, hold your hand about 5 inches above the grill grid; count how many seconds you can comfortably leave it there. When you can hold it there for 2 to 3 seconds, you have medium-high heat and are ready to grill. If you are using a gas grill, heat the grill for 15 minutes with the lid closed. Before beginning to cook, reduce the temperature by turning the knobs to medium-high.

3. Place potatoes on grill and cook, turning, until grill marks appear.

4. Meanwhile, in a large bowl, whisk together mustards, pickled green garlic, pickling liquid, and olive oil.

5. Transfer grilled potatoes to large bowl and gently toss to combine. Garnish with herbs and serve.