I live in Britain but occasionally cook from American recipes, and own measuring cups. While measuring out flour and liquids is straightforward, I'm always stumped when recipes specify a measure of vegetables. For example, '2 TBS carrot' or '2/3 cups carrot' (like the Marcella Hazan bolognese) or '1/2 cup tomates', or grated carrots for cake. How do you know how to chop and measure them? Not all recipes are clear in how finely they're chopped, and the finer a vegetable (or cheese) is chopped, grated or pureed, the more you can pack into a cup (whereas 100g of carrots is 100g no matter how you slice them). Obviously if the measurement is small the difference won't be off by much, but still, I am curious.
How do you measure your vegetables and fruits in cups, especially if they need to be chopped?