In a medium saucepan, bring the water or vegetable broth to a boil over medium-high heat.
Gradually whisk in the polenta, reducing the heat to low. Continue to whisk constantly to avoid lumps. Cook the polenta for about 5 minutes, or until it begins to pull away from the sides of the pan and is thickened.
Stir in the grated Parmesan cheese, olive oil, salt, and black pepper. Mix until the cheese is melted and the polenta is well combined.
Transfer the polenta to a baking dish or pan, spreading it out evenly. Let it cool to room temperature, then refrigerate for at least 1 hour or until firm.
Once the polenta is firm, cut it into 8 slices or squares.
Preheat the grill or grill pan to medium-high heat. Brush the grill grates or grill pan with a little olive oil to prevent sticking.
Grill the polenta cakes for 3-4 minutes on each side, or until they are golden brown and have grill marks.
Remove the grilled polenta cakes from the grill and garnish with fresh herbs if desired.
Serve warm as a side dish, appetizer, or main course, and enjoy with your favorite toppings or sauces.