In a large pot over medium heat, warm the olive oil. Add the white and light green parts of the scallions, garlic, and ½ teaspoon salt. Cook until softened, stirring often, about 2 minutes.
Add the tomato paste, smoked paprika, cumin, and pepper and cook, stirring constantly, for about 30 seconds to toast the spices.
Stir in the water, farro, beans, soy sauce and remaining 1 teaspoon salt. Bring to a boil over high heat, then reduce to medium-low to maintain a simmer for 20 minutes, or until the farro is cooked through, stirring halfway.
Increase heat to medium-high and bring to a boil. Very slowly pour in the whisked eggs (see note). Turn off the heat and let it sit until the eggs become mostly cooked, about 30 seconds (the heat of the broth will continue to cook the eggs). Give the soup a stir to combine.
Serve topped with a dollop of yogurt, the green parts of the scallions, black pepper, a drizzle of olive oil, and a squeeze of lemon.