Place potatoes in a pot of salted water with bay leaf, the sprig of lemon thyme, and black peppercorns; bring to a boil. Reduce heat to a simmer and cook until just tender, about 20 to 25 minutes. Drain well and smash each potato until slightly flattened.
In a large bowl, combine olive oil, lemon juice, lemon zest, the 1 1/2 teaspoons chopped lemon thyme, and the salt and pepper. Toss potatoes gently in olive oil mixture to coat, making sure to not break the potatoes.
Heat a grill pan over medium-high heat. Grill potatoes, in batches if necessary, until a slight crust forms and potatoes are golden brown. Transfer to a large bowl.
In a small bowl, combine mayonnaise, green onions, parsley, mustard and chives; mix well. Spoon the mayonnaise mixture over the potatoes and toss gently until evenly coated.
Serve warm or at room temperature.
If a grill pan is not available, the potatoes can be roasted in the oven until crispy.