In a heavy saucepan, bring the water to a boil over high heat. Add 2 teaspoons salt and the nutmeg and reduce the heat to the medium. Add the polenta gradually, whisking constantly. Continue to whisk for 5 minutes as the mixture bubbles. Reduce the heat to low and cook, stirring occasionally, until the mixture begins to come away from the sides of the pan, about 10 minutes. Add 1/2 cup of the Parmesan cheese, 1 teaspoon thyme and 1/2 teaspoon pepper and stir to combine thoroughly.
Invert a rimmed baking sheet on a countertop and cover the surface with parchment paper. Spread the polenta out with a spatula into a smooth, even layer. Cover the polenta with another sheet of parchment paper. Place another baking sheet, right side up, on top of the parchment. With 2 hands, press down evenly on the top baking sheet until the polenta is 1/4 inch thick. The idea is to sandwich the polenta between 2 flat surfaces. Refrigerate for at least 1 hour or up to overnight.
Preheat the oven to 375 degrees F. Invert the baking sheets together. Remove the top baking sheet and the top layer of parchment paper. The smoother side of the polenta will be facing up. Cut the polenta into triangle about 2 inches long by 1 1/2 inches wide. Transfer the triangles to 1 or more baking sheets, spacing them 1/2-inch apart. Sprinkle about 1/2 cup of the remaining Parmesan cheese and the remaining thyme on top of triangles.
Bake the crostini until hot throughout and starting to brown, about 10 to 12 minutes. Turn the oven to broil and broil the crostini about 8 inches from the heat source until crispy and golden brown on top, about 3 minutes. Serve warm or at room temperature.