Heat half the oil in a large saucepan over medium heat until shimmering. Add the onion and cook until softened and lightly browned, 5 to 7 minutes.

Stir in the farro and cook until the grains are lightly toasted and fragrant, about 2 minutes.

Stir in the broth and water and bring to a simmer. Reduce the heat to low and continue to simmer, stirring often, until the farro is just tender and the remaining liquid has thickened into a creamy sauce, 20 to 25 minutes.

Remove from the heat, stir in half of the Parmesan, and season with salt and pepper to taste.

Bring a large pot of salted water to a boil in a Dutch oven. Add the broccoli rabe and cook until just tender and bright green, about 2 minutes. Drain well and transfer to a bowl.

Wipe the Dutch oven dry, add the remaining oil, garlic, and pepper flakes, and cook over medium heat until fragrant and sizzling, 1 to 2 minutes.

Add the drained broccoli rabe back to the pot and cook until hot and well coated, about 2 minutes. Remove from the heat and stir in the beans, prepared farro mixture, and sun-dried tomatoes. Season with salt and pepper.

Position an oven rack 6 inches from the broiler element and heat the broiler. Transfer the mixture to a 3-quart broiler-safe casserole dish and sprinkle with the remaining Parmesan.

Broil until the cheese is lightly browned and the mixture is bubbling, 3 to 5 minutes. Let the dish rest for 5 minutes before serving.