Preheat the oven to 425°F. Line a rimmed sheet pan with parchment paper.

On the prepared pan, toss together the potatoes, 2 tablespoons of oil, and ¼ teaspoon salt to coat. Arrange the potatoes cut-side down. Roast until browned on the bottom and the skin is puckered on top, 20 to 25 minutes. Add the olives to the pan and bake for 3 minutes more, or until the olives are heated through and juicy. Set aside.

While the potatoes roast, place the tuna steaks in a medium bowl with 2 tablespoons of oil, the garlic, thyme, and lemon zest. Season lightly with salt and slosh the steaks around until coated well, rubbing the garlic and thyme onto the steaks. Set aside at room temperature.

In a large heavy-bottomed skillet like cast iron, heat a thin layer, about ⅛ inch of oil over medium-high heat. Add the green beans and shallot. Sauté until the beans are al dente, about 5 minutes. If the beans are charring but not getting cooked through, add a few tablespoons of water and they will steam. Season with salt and transfer to a plate.

Wipe out any remnants of shallot from the skillet and add another thin layer, about ⅛ inch of oil. Raise the heat to high. Once the oil is just shy of smoking, add the tuna steaks, leaving behind the garlic and thyme sprigs. Sear until the bottom is browned, but the fish isn’t opaque all the way up the sides, about 2 minutes. Flip the steaks and repeat on the opposite side for 1 minute for medium-rare, or longer if you want it cooked through. Transfer the tuna to a work surface and let rest for a few minutes before slicing.

Assemble the salad. On a large serving platter, scatter the arugula and radicchio. Pile the crispy potatoes and olives, sautéed green beans, and tuna slices in sections. Drizzle with half the dressing and serve the remainder on the side.