Combine 2 tablespoons olive oil, 2 grated garlic cloves and the chopped rosemary in a small bowl. Pierce the steak all over with a fork; rub with the garlic oil. Let marinate 10 minutes.
Meanwhile, heat 1 tablespoon olive oil in a medium saucepan over medium-high heat. Add the remaining 1 grated garlic clove and cook, stirring occasionally, until softened, about 30 seconds. Add the beans and their liquid, the rosemary sprig and 1/2 cup water. Bring to a boil, then reduce the heat to a simmer and cook, stirring occasionally, until slightly thickened, about 5 minutes. Season with salt and pepper. Cover and set aside to keep warm.
Meanwhile, toss the red onion and lemon juice in a large bowl; set aside. Heat a grill pan over medium-high heat; brush with olive oil. Season the steak with salt and pepper and grill until marked and cooked through, 5 minutes per side. Transfer to a cutting board.
Add the arugula and the remaining 2 tablespoons olive oil to the bowl with the onion; season with salt and pepper and toss. Discard the rosemary sprig from the beans and stir in the parsley; thin with water if needed. Slice the steak against the grain and serve with the beans. Top each serving with the arugula salad and parmesan.
Photograph by Ryan Dausch