Trim the dark green ends off of the leeks (don’t throw away). Cut the leek bottoms in half lengthwise and rinse well under cold water to remove any debris in layers. Rinse the dark tops as well. Thinly slice the leeks.
In a large pot or large skillet with a lid, warm the oil and butter over medium-high heat. Add the leeks and ½ teaspoon salt and cook until caramelized and browned, about 10-15 minutes, stirring occasionally. The longer you cook the leeks, the better. If you’re in a hurry you could just cook until they just begin to brown and soften (5 minutes minimum).
Stir in the tomato paste, fennel, pepper, red pepper flakes, garlic, and cook for about 3 minutes or until tomato paste is caramelized (color has darkened and is sticking to the bottom of the pot), stirring occasionally.
Stir in the water, farro, soy sauce, and remaining ½ teaspoon salt and scrape the bottom if anything is stuck. Cover with a lid, bring to a boil over high heat, then reduce the heat to medium-low to maintain a rapid simmer for 30 minutes or until the farro is cooked. If farro is not cooked and water is low, just add a splash of boiling or hot water and continue to cook.
Serve topped with cheese, egg, herbs, lemon zest and juice, and sprinkle with salt and pepper.