Grease and line a 6 inch cake pan. Preheat the oven to 340°F / 170°C for at least 15 minutes.

Mix the milk, vinegar, sugar, vanilla, and oil until smooth and the sugar dissolves completely.

Fluff the flour in its container, spoon it into the measuring cup, and level it.

Sift the flour, baking soda, baking powder, cinnamon, nutmeg, and salt into a bowl. Mix well.

Stir the milk mixture again, pour it into the dry ingredients, and mix only until combined and lump-free.

Add the grated carrot and fold gently until just combined.

Pour the batter into the pan and tap the pan twice on the counter.

Bake for 28 to 30 minutes, until a tester inserted in the center comes out clean.

Cool the cake in the pan on a rack for 10 minutes, then invert onto the rack and cool completely before slicing or frosting.

Beat the cream cheese with softened butter until smooth.

Add powdered sugar and vanilla, then beat until smooth, light, fluffy, and spreadable. Add more sugar to taste. If too thick, add 1 tablespoon milk; if too thin, add a little powdered sugar.

Spread the frosting over the cooled cake and sprinkle with chopped nuts or toasted coconut.