Heat oven to 400° F.
Mix the bread crumbs, rosemary, 1/2 teaspoon salt, 1/4 teaspoon pepper, and 3 tablespoons of the oil in a large bowl. Add the shrimp and toss to coat. Transfer shrimp and any excess crumbs to a baking sheet. Bake until the shrimp are cooked through and the bread crumbs are crispy, 10 to 12 minutes.
Heat the remaining oil in a medium skillet over medium-high heat. Add the garlic and cook, stirring, for 30 seconds. Add the beans, 1/4 cup water, 1/4 teaspoon salt, and 1/4 teaspoon pepper. Cook until heated through, about 2 minutes. Remove from heat, add the arugula, and toss to combine.
Divide the beans among individual plates and serve with the shrimp. Sprinkle any extra bread crumbs from the pan over the top.
Substitution: If fresh rosemary is not available--or not one of your favorite herbs--use sage or thyme instead.