Preheat the oven to 425 degrees F. Line a baking sheet with foil. Toss the fennel and tomatoes with 2 tablespoons olive oil and season with salt and pepper. Spread the vegetables on the baking sheet, with the tomatoes cut-side up. Roast until the tomatoes are soft and the fennel is golden, about 30 minutes, turning halfway through.
Meanwhile, cook the garlic in the remaining 1 teaspoon olive oil in a medium saucepan over medium heat until golden, about 3 minutes. Add the beans and 2 1/2 cups water and cook, stirring occasionally, until the liquid thickens, about 15 minutes. Stir in the oregano and parmesan, if desired.
Heat a grill pan over medium-high heat. Season the lamb with salt and pepper and grill until marked on the bottom, about 4 minutes. Flip and cook until just firm to the touch, 4 to 5 more minutes for medium-rare. Divide the beans among plates and top with the lamb and roasted vegetables.