To prepare chicken, combine first 13 ingredients in a large Dutch oven; bring to a boil. Reduce heat, and simmer 15 minutes. Sprinkle 1/2 teaspoon salt and 1/4 teaspoon black pepper over chicken; add chicken to pan. Bring to a boil; reduce heat, and simmer 5 minutes. Remove pan from heat. Cover and let stand 30 minutes. Remove chicken from pan with a slotted spoon; cut into 1/4-inch-thick slices. Reserve poaching liquid for another use.
To prepare salsa verde, combine the cilantro and next 9 ingredients (through 3 minced garlic cloves), stirring until well blended.
To prepare vegetables, heat 2 teaspoons oil in a large nonstick skillet over medium-high heat. Add shallots and next 5 ingredients (through 3 garlic cloves) to pan; sauté 1 minute. Add kohlrabi and radishes; sauté 2 minutes. Stir in 1/2 cup broth; bring to a simmer. Cook 8 minutes or until vegetables are almost tender. Add bok choy; cook 2 minutes or until vegetables are tender. Serve with chicken and salsa.