Preheat the oven to 350°F and butter an 8-inch square baking pan.

Spread the farina on a rimmed baking sheet and toast until it smells aromatic and looks lightly browned, about 15 minutes.

Whisk the sugar, salt, coconut milk, and water in a large pot over medium heat until the sugar dissolves completely—this should take about 4 minutes, though palm sugar may take slightly longer.

Whisk the eggs in a separate bowl. Temper the eggs by slowly drizzling in a small portion of the hot coconut liquid while whisking constantly; once incorporated, stir the egg mixture back into the main pot and cook for 1 minute.

Whisk the toasted farina into the liquid gradually to prevent lumps. Switch to a rubber spatula and cook over medium heat, stirring frequently for 4 to 5 minutes, until the batter thickens and a thin film begins to form on the bottom of the pot.

Stir in the peanut oil until fully incorporated.

Pour the batter into the prepared pan and sprinkle the poppy seeds evenly across the surface.

Bake until the cake is lightly set and the sides are bubbling, about 35 minutes.

Dot the top of the cake with butter and return it to the oven for 5 minutes to allow the butter to melt and soak into the top.

Let the cake cool in the pan for at least 30 minutes before cutting into rectangles. Serve at room temperature when the texture has fully set and turned chewy.