Heat olive oil in a large pot over medium heat. Add chicken, onion, and crushed garlic cloves; cook until chicken is browned and onion turns translucent, about 5 minutes.

Pour water, wine, and lemon juice over chicken mixture; stir in sliced ginger, sugar, bouillon cubes, bay leaves, and peppercorns. Bring to a simmer, then reduce heat to medium-low and cook for 45 minutes.

Remove and discard garlic cloves. Transfer chicken to a cutting board and chop into bite-size pieces.

Add carrots, celery, kohlrabi, rosemary, and thyme to the pot. Reduce heat to low and cook until vegetables soften, about 20 minutes.

Bring soup to a boil. Return chopped chicken to the pot along with egg noodles, minced garlic, and grated ginger. Remove from heat and let sit until pasta has softened, about 10 minutes.