Step 1

Trim dark green top from leek; discard. Slice white and pale green parts ½" thick. Place in a large bowl, cover with water, and rinse, separating rings to remove dirt. Drain; pat dry.

Step 2

Heat oil in a large pot over medium. Cook half of the leek, stirring occasionally, until softened, about 2 minutes. Add garlic, ¼ cup curry paste, and 2 Tbsp. Diamond Crystal or 1 Tbsp. plus ½ tsp. Morton kosher salt. Cook, stirring occasionally to coat leek, until fragrant and curry is brick red, about 2 minutes. Add broth, tahini, honey, soy sauce, vinegar, and 2 cups water and stir to combine. Increase heat to high and bring liquid to a boil. Reduce heat to low, cover pot, and simmer 20 minutes. Taste soup; stir in more curry paste and season with more salt if desired.

Step 3

Meanwhile, cook noodles in a large pot of boiling salted water according to package directions, stirring occasionally, until al dente. Drain and set aside.

Step 4

Add kale, butter, and remaining leek to soup and simmer, uncovered, stirring occasionally, until kale and leek are softened, 5–7 minutes.

Step 5

Divide reserved egg noodles among bowls; ladle soup over.