In a large saucepan, heat the olive oil over medium heat. Add the garlic, onions and chile flakes and cook until the onions soften, about 3 minutes. Add the orzo and white wine and cook until the wine is absorbed, 2 to 3 minutes. Add the chicken broth, some salt and pepper and 2 cups water and bring to a simmer. Cook, stirring often, until the orzo is tender and cooked through, about 20 minutes.
Stir in the arugula, Parmesan and butter and serve.