Boil the chicken, kamaboko, leeks, and carrots in the dashi stock until half-way cooked. Remove.
Next, add the udon to the stock and boil until it reaches a chewy consistency. Then add the hatcho miso and continue to cook. As soon as the stock returns to the boil, remove the udon and place in four deep soup bowls.
Break the eggs into the stock (perhaps in two batches), and poach until half-way done. While the eggs are cooking, distribute the chicken, kamaboko, spinach, and other vegetables over the udon.