Peel the potatoes and slice them into thin 1/8-inch thick slices. Put them into a large bowl and toss with the thyme, rosemary, and olive oil; season with salt and pepper. Place a large skillet onto the grill and coat the bottom with olive oil. Place the slices into the pan, overlapping them in 1 layer until the entire surface is covered with potatoes. Drizzle some more olive oil over the top. Cook over medium-high heat until the bottoms are browned and crisp. Turn the potatoes over and cook the other side until they are browned and crisp.

In a food processor add the olives, capers, garlic, and parsley. Process, adding some olive oil in a thin stream, until you have a smooth puree. Mix in the lemon juice and adjust the seasoning with salt and pepper.

Coat the bottom of a large platter with some of the salsa, pile the potatoes on top, and drizzle on some more salsa.