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Step 1
Season chicken thighs on all sides with salt and pepper. Put oil in a heavy-bottomed soup pot over medium high heat. Add thighs and cook for 3 to 4 minutes, reducing heat to keep meat from browning. Turn and cook other side for about 2 minutes.
Step 2
Add garlic and ginger and let sizzle without browning. Add mirin, sugar, tamari and 8 cups water, then bring mixture to boil. Lower heat and simmer gently for 20 minutes. Turn off heat. Remove thighs and chop into 1/2-inch chunks, then return meat to pot. Taste broth and adjust salt if necessary.
Step 3
In a separate pot, cook buckwheat noodles according to package directions, being careful not to overcook. Drain noodles and refresh with cool water, then leave at room temperature.
Step 4
Bring a small pot of salted water to boil. Add snap peas and leeks and simmer 1 minute, then drain and refresh with cool water. Leave at room temperature.
Step 5
To serve, reheat broth to just under a boil. Dilute miso with a little hot broth and whisk into soup. Add spinach and let wilt slightly, then add leeks and snap peas and let them warm for 1 minute. Divide the noodles among 6 warmed bowls and ladle soup over. Top each bowl with a little basil.