Preheat oven to 425.F. Prepare an 8x8" baking dish.
Toast semolina in a large dry skillet over medium-high heat until beginning to darken and smell nutty. Let cool.
Whisk egg, coconut milk, half-and-half, sugar, salt, and 1 Tbsp. butter in a large saucepan. Gradually whisk in semolina and bring mixture to a boil over medium-high heat, whisking, until mixture is very thick and pulls away from the sides of the pan. Scrape batter into prepared dish.
Bake until golden brown and a tester comes out clean.
Transfer pan to rack and brush with remaining butter. Serve warm.
Made in a cake pan, resulting in a slightly thinner cake that was cooked through and golden in about 35 minutes. The 'batter' was very thick and can't be described as 'pourable'. The resulting cake is not very sweet and almost custard-like in texture. Serving with vanilla ice-cream made it very good, but I don't think I would enjoy it alone.