Bring a large pot of salted water to a boil. Boil farro until tender, about 12 to 15 minutes, and drain in colander. Spread farro out on plate or baking dish and put in fridge to cool.
Meanwhile, toast sunflower seeds in a large non-stick sauté pan over medium-low heat until golden brown, about 5 to 7 minutes. Transfer sunflower seeds to a plate or bowl to cool and wipe pan clean.
In large mixing bowl combine farro, sunflower seeds, cherry tomatoes, arugula, basil leaves, and shaved parmesan.
In the same large non-stick sauté pan heat olive oil, rosemary, and garlic cloves over medium high heat. Carefully add eggs to hot oil, season with salt and pepper, and baste with olive oil until desired doneness is reached. Remove eggs from pan, discard garlic and rosemary and allow remaining olive oil to cool slightly.
Add remaining olive oil to farro mixture along with lemon juice and toss to combine. Season to taste with kosher salt and freshly cracked black pepper.
To serve, divide farro mixture evenly on plates and top each salad with a fried egg. Any remaining farro mixture will keep in the refrigerator for up to 3 days.