Slice the baby potatoes into 1/2-inch thick rounds. Bring a pot of salted water to a boil and add the potato slices. Boil for about 12 minutes or until fork-tender yet firm. Drain and pat dry.

In a mixing bowl, whisk together olive oil, 2 tablespoons of lemon juice, thyme, mustard, salt, and pepper. Add the dried potatoes and toss to coat.

Combine mayonnaise, remaining lemon juice, honey, and smoked paprika in another bowl. Whisk until smooth and creamy.

Preheat grill to medium-high heat and lightly oil the grates to prevent sticking.

Carefully place the marinated potato slices on the grill. Cook for 5 to 10 minutes, turning halfway for even charring.

Transfer warm potatoes to a bowl, drizzle the dressing, and gently toss. Mix in thyme, green onions, dill, and capers.

Let rest for a few minutes before serving warm or at room temperature.