Bring water to a boil in a heavy saucepan over high heat.

Add salt and nutmeg, then reduce heat to medium.

Gradually add polenta while whisking constantly for 5 minutes until bubbling.

Reduce heat to low and cook, stirring occasionally, until mixture pulls away from sides (about 10 minutes).

Stir in Parmesan cheese, thyme, and pepper to combine.

Invert a rimmed baking sheet and cover with parchment paper.

Spread polenta into a smooth, even layer.

Cover polenta with another sheet of parchment paper.

Place another baking sheet on top of the parchment.

Press down evenly until polenta is 1/4 inch thick.

Refrigerate for at least 1 hour or up to overnight.

Preheat oven to 375 degrees F.

Invert baking sheets together and remove top baking sheet and top parchment paper.

Cut polenta into triangles about 2 inches long by 1 1/2 inches wide.

Transfer triangles to baking sheets, spacing 1/2-inch apart.

Sprinkle remaining Parmesan cheese and thyme on top.

Bake until hot and starting to brown, about 10-12 minutes.

Turn oven to broil and broil until crispy and golden brown, about 3 minutes.

Serve warm or at room temperature.