In a large bowl, combine the beef, onion, garlic, salt, and pepper. Knead the mixture thoroughly by hand for 3 to 4 minutes, until tacky and cohesive. Divide into 4 to 6 portions and shape each one tightly around a flat metal skewer to form even kebabs.
Heat a grill or heavy skillet over medium-high heat until very hot. Lightly oil the grates or pan. Grill the kebabs for 2 to 3 minutes per side, turning once, until browned and cooked through. Transfer to a plate and let rest.
Place the radish slices in a bowl of ice water for 15 minutes. Drain and pat dry.
In a large bowl, combine the red onion, green onions, radishes, chili (if using), and crushed tomato. Add the lemon juice, olive oil, salt, and pepper. Toss well, then gently press the mixture with your hands or the back of a spoon to soften and release flavor.
In a small bowl, whisk together the tahini, lemon juice, and amba until smooth and creamy. If too thick, whisk in a splash of cold water until the texture is thick but spoonable.
Split the baguettes or rolls. Spread a generous layer of tahini sauce on the bottom halves. Add a kebab, top with salad, and add another kebab if desired. Drizzle more tahini sauce on top and finish with extra salad. Close the sandwich, wrap tightly in parchment paper, slice in half, and serve immediately.