Rinse the farro, then simmer it in the broth until tender, 25–30 minutes; drain any excess and cover to steam.
Heat 1½ tbsp olive oil in a large skillet over medium-high. Sear mushrooms until browned, 6–8 minutes, seasoning with a pinch of salt.
Stir in butter, shallot, garlic, and thyme. Cook until fragrant and softened, about 2–3 minutes.
Deglaze with soy sauce, then fold in spinach to wilt. Finish with lemon juice and a few grinds of pepper.
In a nonstick pan, warm the remaining oil. Fry the eggs to your liking; leave yolks runny if desired.
Add cooked farro to the mushroom skillet. Toss with Parmesan, red pepper flakes, remaining salt, and more pepper to taste.
Spoon farro into bowls. Top each with an egg, extra Parmesan, and scallions. Serve hot.