Sort beans for debris, then rinse. Bring beans and 6 cups water to a boil over high heat in a 5- to 6-quart pan. Cover, boil for 2 minutes, and remove from heat. Beans are ready to cook after soaking for 2 hours, but are more digestible after 4 hours. Drain and rinse beans.
Brown meat in 1 teaspoon oil in a 10- to 12-inch frying pan over medium-high heat, turning as needed, about 20 seconds per side. Discard oil.
Lift meat to a 9-inch baking pan. Bake in a 350° oven until a thermometer inserted into side of a steak reaches 128°, 20 to 25 minutes. Let meat cool, then chill airtight until cold, about 1 hour.
Combine sage, thyme, and oregano; set aside 3 tablespoons of the mixture. Thinly slice meat across the grain and place in the 9-inch pan. Mix with 2 tablespoons oil, then sprinkle evenly with remaining herbs, salt, and pepper. Chill airtight at least 30 minutes or up to 4 hours.
While meat cooks and cools, bring beans and 2 quarts water to a boil over high heat in a 5- to 6-quart pan. Reduce heat and simmer, covered, for 40 minutes. Add 1 teaspoon salt and 1/2 teaspoon pepper. Simmer until beans are just tender to bite, 30 to 40 minutes. Drain; transfer to a bowl.
In a 6- to 8-inch frying pan over medium heat, stir remaining oil and the garlic until garlic is pale golden, about 2 minutes. Stir in reserved herb mixture. Combine with beans. Add lemon juice. If making ahead, chill airtight up to 4 hours.
Bring meat (and beans, if chilled) to room temperature. Arrange arugula in a wide bowl. Spoon beans and then beef on top. Garnish with parmesan and serve with lemon wedges to squeeze over salad.