Preheat an oven to 400 degrees F.
Trim any green leaves from the cauliflower and invert it on a cutting board. Slicing through the core, cut four steaks about 1/2-inch thick from the center of the vegetable. Reserve any florets that fall away for later use.
Place a large skillet over medium-high heat with about 1 tablespoon of olive oil. Working in batches as needed, cook the steaks until well caramelized, about 3 minutes per side. Transfer the browned steaks to a baking sheet and continue browning the remaining batches, adding a tablespoon of olive oil to the pan with each new batch. Bake the cauliflower steaks in the oven until tender, 6 to 8 minutes. Season with salt and pepper and reserve.
While the cauliflower steaks are baking, in a large mixing bowl combine all of the ingredients for the beans and tomatoes, seasoning as needed with salt and pepper. Reserve.
Serve the cauliflower steaks warm or at room temperature with the beans and tomatoes.