In a medium heavy-bottomed saucepan, combine 3 cups water, 1 cup whole milk and 1 teaspoon salt. Bring to a gentle simmer over medium heat. Do not boil vigorously; a steady simmer is fine.

Whisk in polenta

Gradually whisk in 1 cup coarse cornmeal (polenta) in a slow, steady stream to prevent lumps. Reduce heat to low immediately after adding the cornmeal.

Cook polenta

Cook, stirring frequently (use a heatproof spatula or wooden spoon), until the polenta thickens and pulls away slightly from the sides of the pan, about 20–25 minutes for coarse polenta. If the mixture becomes too thick, add up to 2–4 tablespoons warm water or milk to maintain a smooth consistency.

Finish with butter and cheese

Stir in 2 tablespoons unsalted butter, 1 tablespoon grated Parmesan, and 1 teaspoon freshly ground black pepper until incorporated. Taste and adjust salt as needed.

Set the polenta

Line an 8x8-inch (or similar) shallow pan or baking dish with plastic wrap or parchment. Pour the hot polenta into the prepared pan and spread it evenly to about 3/4-inch (approx. 2 cm) thickness. Smooth the top with a spatula. Cover the surface with plastic wrap (to prevent a skin) and refrigerate until fully set, at least 2 hours or up to overnight.

To Fry & Finish

Prepare for frying

When the polenta is firm, remove it from the pan by lifting the plastic wrap or inverting the dish. Slice the chilled polenta into 1/2- to 3/4-inch thick rounds or rectangles (about 8–10 pieces from an 8x8 pan). Pat pieces dry with paper towels to remove surface moisture—this helps get a crisp crust.

Heat the pan

Heat a large nonstick or cast-iron skillet over medium-high heat. Add 3 tablespoons olive oil and 1 tablespoon unsalted butter (optional for richer flavor). When the oil shimmers and the butter foams but before it browns, the pan is ready.

Fry the polenta

Working in a single layer (do not crowd the pan), add the polenta pieces and fry until deep golden-brown and crisp, about 3–4 minutes per side. Use a thin spatula to carefully flip the pieces. If browning too quickly, reduce heat to medium. Add a little more oil between batches if needed.

Drain and season

Transfer fried polenta to a wire rack or plate lined with paper towels to drain briefly. Immediately sprinkle with a pinch of sea salt (about 1/8–1/4 teaspoon per piece depending on size).

Finish and serve

Arrange fried polenta on a serving plate. Sprinkle with chopped fresh herbs (about 1 tablespoon) and an additional 2 tablespoons grated Parmesan if desired. Serve hot as a side, appetizer with a dipping sauce, or topped with braised mushrooms, tomato sauce, or a fried egg.