In a medium saucepan, cover the potatoes with cold water and bring to a boil. Reduce the heat to a simmer, cover, and cook for 30 minutes, or until tender.
Meanwhile, preheat the oven to 300°F. Drain the potatoes, reserving 1 cup of the liquid; let the water cool to room temperature. Place the potatoes on a baking sheet and let dry in the oven for 10 minutes.
Meanwhile, in a small bowl, sprinkle the yeast over the warm water. Stir in the brown sugar or honey until dissolved and let stand until foamy, about 10 minutes.
Peel the potatoes and place them in a large bowl; beat with an electric mixer or use a potato masher to mash them. Stir in the reserved potato water and 2 tablespoons of the olive oil. Add the yeast mixture, herbs, 1 cup of the flour, and the salt and mix until smooth. Stir in the remaining 2½ cups flour ½ cup at a time until the dough comes together in a loose ball. On a floured board, knead the dough until smooth and elastic, 8 to 10 minutes. The dough will be quite soft.
Put the dough in an oiled bowl, turn to coat, and cover with plastic wrap or a damp tea towel. Let rise in a warm place until doubled, about 1½ hours. Punch the dough down, turn it out onto a lightly floured board, and knead a few times to eliminate air bubbles. Roll the dough into a rectangle about 10 by 14 inches and place on an oiled baking sheet. Use a dough scraper or clean razor blade to make 4 or 5 diagonal cuts, each about 4 inches long, slanting downward on one side of an imaginary center line. Make matching cuts on the other side of the line. Open the cuts by pulling gently. Do not cut through or tear the encircling piece of dough. Brush with the remaining 1 tablespoon olive oil and stud the surface with the olives. Cover with a tea towel and let rise until doubled.
Preheat the oven to 425°F. Bake for 20 to 25 minutes, or until golden brown. Transfer the loaf to a wire rack and let cool. Serve warm or at room temperature, and pull apart to serve.