Heat oven to 400° F. In a bowl, mix the bread crumbs, rosemary, 3 tablespoons oil, ½ teaspoon salt, and ¼ teaspoon pepper. Add the shrimp and toss to coat.
Transfer the shrimp and any excess crumbs to a baking sheet. Bake until the shrimp are cooked through and the crumbs are crispy, 10 to 12 minutes.
Meanwhile, heat the remaining oil in a medium skillet over medium-high heat. Add the garlic and cook, stirring, for 30 seconds. Add the beans, ¼ cup water, and ¼ teaspoon each salt and pepper. Cook until heated through, 2 to 3 minutes.
Remove from heat and toss with the arugula. Serve the beans with the shrimp and sprinkle any remaining crumbs over the top.