Warm the olive oil in a medium, heavy-bottomed saucepan over medium heat. Add the finely diced onion and cook, stirring occasionally, for 4-5 minutes until completely softened and translucent. You are not looking for colour here - the goal is sweetness, not browning. If the onion begins to take on any colour, lower the heat slightly.
Add the dried trahanas directly to the pot with the softened onion. Stir everything together and cook for about 1 minute, turning the grains through the oil. This brief step is easy to skip but worth doing: the gentle heat deepens the flavour of the grain and helps it absorb the broth more evenly once the liquid goes in.
Pour in the chicken broth and water. Stir well, making sure no trahanas is clinging to the bottom or sides of the pot. Increase the heat to medium and bring the liquid to a gentle simmer - you want small, steady bubbles at the surface, not a rolling boil.
Reduce the heat to medium-low. Cook uncovered for 18-22 minutes, stirring every 3-4 minutes, until the soup has thickened to a consistency somewhere between a light porridge and a cream soup. It should coat the back of a spoon and hold a moment when you run your finger through it. If it becomes thicker than you like before the time is up, add a splash of hot water and stir.
Taste and season carefully with salt and pepper. Remember that the feta on top will also contribute saltiness, so season conservatively at this stage. Ladle into warmed bowls. Top each bowl generously with crumbled feta, a drizzle of good olive oil, and a pinch of dried oregano or a few thyme leaves. Serve immediately, with crusty bread alongside.
