Heat the olive oil in a large pot over medium heat. Add the lamb cubes and brown them on all sides, about 5 minutes. Remove the lamb and set it aside.
Add the onion to the same pot and cook until softened, about 4 minutes. Stir in the garlic, curry powder, and cumin. Cook for 1 minute until fragrant.
Return the lamb to the pot. Add the diced tomatoes, chicken broth, and pearl barley. Season with salt and pepper. Bring the mixture to a boil.
Reduce the heat to low, cover the pot, and simmer for 45 minutes until the barley is tender and the lamb is cooked through.
Stir in the spinach and cook just until it wilts, about 2 minutes. Remove the pot from the heat.
Ladle the stew into bowls and top each serving with a generous spoonful of plain yogurt.