Preheat the oven to 425°F.
Place the farro in a small saucepan with a big pinch of salt and cover with water by 1 inch. Bring to a simmer, reduce heat to medium-low, cover, and simmer until the grains are tender, about 40 minutes. Drain the farro and return to the saucepan. Toss with olive oil.
On a baking sheet, toss the mushrooms, oil and salt. Roast until crisp on the edges, about 20 minutes. Toss the mushrooms with the cooked farro.
Bring a large, shallow skillet of salted water to a bare simmer. Crack each egg into a ramekin then gently add the eggs one at a time to the simmering water and cook until the white is just set. Immediately remove from the water to a bowl of warm water.
In a blender, purée the parsley, garlic, balsamic and oil until smooth. Transfer to a bowl, along with the remaining salsa verde ingredients and season to taste.
Divide the farro and mushrooms between bowls. Top with poached eggs, arugula, fried garlic chips, onions and salsa verde.