Preheat the oven to 400° and oil an 8-inch round cake pan, preferably of dark metal. Line the bottom of the pan with parchment paper and oil the paper.
In a medium saucepan, heat the 1 1/2 tablespoons of olive oil. Add the shallot and cook over moderate heat, stirring occasionally, until softened, about 3 minutes. Add the thyme and rosemary and cook for 1 minute. Add the chicken broth and bring to a boil. Cook over moderately high heat until reduced to 3/4 cup, about 10 minutes.
Arrange an overlapping layer of potato slices in the cake pan. Season lightly with salt and pepper and spoon a small amount of the reduced broth on top. Repeat the layering with the remaining potatoes and reduced broth, seasoning each layer lightly. Pour any remaining broth on top. Cover the pan with a sheet of oiled parchment paper and then a sheet of foil.
Bake the gratin in the center of the oven until the potatoes are very tender, about 1 hour. Remove the foil and paper and bake until the top is dry, about 10 minutes longer.
Turn the broiler on. Remove the gratin from the oven and let rest for 5 minutes. Invert the gratin onto a heatproof plate. Carefully remove the parchment round. Broil the gratin 6 inches from the heat until the surface is lightly browned, about 2 minutes. Cut into wedges and serve.