Put the wheat berries in a medium saucepan and fill the pan with cold water (as if you were making pasta.) Add a big pinch of salt (kosher is fine.) Bring the water to a boil and reduce to a simmer. Cook wheat berries until they are tender, about 50-60 minutes. Drain and transfer to a serving bowl to cool slightly.
For the dressing: whisk all ingredients together in a medium bowl and season with salt, cayenne and black pepper to taste. Dip a piece of lettuce in the dressing to taste for seasoning.
Combine green onions, radishes and greens with the wheat berries in the serving bowl. Toss with enough dressing to coat lightly.