Buckwheat Soup with Soft-Cooked Eggs

2 whole eggs
1 qt chicken stock
1/4 cup roasted buckwheat groats
aka kasha
sesame oil
2 tsp sesame seeds
preferably a mix of white and black sesame seeds
We found this recipe through the Uniqlo cooking app and tried it out since we had buckwheat groats on hand. It turned out to be a delicious light breakfast that we now make regularly. We adapted the soft-cooked egg technique from Cook's Illustrated. We also adjusted the proportions for eggs and broth to our taste.
In the small pot, bring 1/2-inch of water to a boil over medium heat.
Use a thumbtack to poke a small hole at the rounder end of the eggs. Use tongs to place the eggs in the pot then cover and cook for exactly 6 minutes and 30 seconds.
Shake the eggs in the pot to crack them slightly. Transfer the pot to the sink and run cold water over them for 1 minute then reserve.
In a medium saucepan, bring the chicken broth to a boil then add the buckwheat. Drop the heat to a simmer and cook until the buckwheat is tender but chewy, about 5 minutes. Season to taste with salt.
While the broth simmers, peel the eggs, under running water if needed.
Fill the serving bowls with soup and drizzle with 1-2 drops of sesame oil. Transfer a peeled egg to each bowl of soup. Gently pinch the egg together, then cut the egg in half. Orient each half yolk-side up. Sprinkle with sesame seeds and serve immediately.
source: adapted from a recipe by Kuniko Yagi in the Uniqlo recipe app