Preheat the oven to 375°F (190°C). Lightly grease an 8-inch square baking pan or a similarly sized ovenproof skillet with 1 tablespoon butter or oil. Set aside.

Cook the grits

In a medium saucepan, bring 4 cups water to a gentle boil with 1 teaspoon salt and 1 tablespoon sugar. Slowly whisk in 1.5 cups coarse corn grits. Reduce heat to low and simmer, stirring frequently, until the grits thicken and become creamy, about 15–20 minutes (cooking time depends on grit coarseness). If mixture becomes too stiff, stir in up to 2–4 tablespoons additional water or milk to reach a thick but spreadable consistency.

Enrich the grits

When the grits are tender and creamy, remove pan from heat. Stir in 3 tablespoons unsalted butter, 1 cup whole milk, and 1 tablespoon olive oil until fully incorporated and smooth. Allow the grits to cool slightly for 5 minutes so they are warm but not piping hot.

Mix dry ingredients

In a small bowl, whisk together 1/2 cup all-purpose flour and 1 teaspoon baking powder and 1/4 teaspoon black pepper. This will help the cake set while keeping a tender crumb.

Combine batter

Beat 1 large egg in a small bowl. Stir the beaten egg into the warm (not hot) grits along with the flour/baking powder mixture, 3/4 cup grated sharp cheddar (if using), 2 tablespoons chopped scallions or chives (if using), and 1 teaspoon lemon zest (if using). Mix until just combined. The batter should be thick but spreadable; if excessively stiff, add 1–2 tablespoons milk.

Bake

Spread the grits batter evenly into the prepared pan or skillet, smoothing the top with a spatula. Bake in the preheated oven until the top is golden and a toothpick inserted into the center comes out clean or with a few moist crumbs, about 30–35 minutes. If using a cast-iron skillet, the edges will crisp nicely.

Cool and slice

Remove the pan from the oven and let the cake rest for 10–15 minutes to firm up. Run a knife around the edges and invert onto a cutting board (or slice directly in the pan). Cut into 6 or 8 squares/wedges depending on desired serving size.

Finish and serve

Serve warm or at room temperature. Optional: top with an extra pat of butter, a sprinkle of chopped scallions or herbs, or a dollop of sour cream or yogurt. These cakes also pan-fry beautifully: heat 1 tablespoon oil in a skillet and brown slices 2–3 minutes per side before serving for extra crispness.