Bring a large pot of salted water to a boil. Add the farro and boil for 30 minutes until tender. Drain and rinse and set aside.
Cook the Vegetables:
Melt the butter into a wide pot over medium heat. Add the leeks and mushrooms and cook for 8-9 minutes until the mushrooms are golden brown. Add the garlic and minced chili pepper and cook for 45 seconds until fragrant. Season with salt and pepper.
Simmer the Sauce:
Pour in the stock and bring to a boil. Reduce heat to low and simmer for 20 minutes until reduced.
Finish the Sauce:
Pour in the cream and turn the heat to medium until bubbling, but not boiling. Cook for 5-7 minutes more until the cream is thickened. If you'd like a thinner sauce, add more stock as desired, in 1/4 cup increments.
Add the arugula and crab and cook for 5 minutes until the arugula is just wilted. Add the farro and stir to combine. Cook for 3-5 minutes more until the cream is thickened. Taste and season again to your preferences.
To Serve:
Divide the farro between shallow bowls and garnish with parsley and a drizzle of oil, if desired. Sprinkle with flaky sea salt, optional. Enjoy!