Preheat the oven to 325 degrees Fahrenheit.
Make the croutons: Cut the bread into one-half-inch cubes and put the cubes in a bowl. Add the olive oil, cheese, pepper flakes, and salt and toss to coat. Spread the croutons on a baking sheet and bake until crisp and golden, about 35 minutes. Let cool.
Preheat the grill until hot. Or preheat a grill pan or large cast-iron skillet over medium-high heat on the stove top until it smokes.
Brush both sides of the tuna steaks generously with the olive oil and season with salt and pepper. Arrange on the grill, grill pan, or skillet and cook, turning once, for 2 minutes per side for medium. Transfer to a platter and let stand while preparing the rest of the salad.
Slice the potatoes one-quarter inch thick. Place them in salted water to cover and cook until tender, no more than 10 minutes. Drain in a colander, run under cold water to stop the cooking, and reserve.
Cook the string beans in boiling salted water to cover until crisp-tender and bright green, about 4 minutes. Drain, run under cold water to stop the cooking, and reserve.
Peel, trim, and slice the red onion into one-quarter-inch-thick rings. Soak in cold water to cover for 20 minutes. While the onion is soaking, dice the tomatoes. Tear the radicchio leaves coarsely. Chop the basil leaves.
Peel, trim, and mince the garlic. Mash the anchovy fillets. In a small bowl, combine the garlic and anchovies with the olive oil and vinegar. Set aside until ready to dress the salad.
Slice the grilled tuna. Drain the red onion and pat it dry.
To serve, combine in a large shallow bowl the radicchio, tomatoes, potatoes, string beans, red onion, basil, and capers. Add the tuna and dressing and toss to combine. Taste and adjust the seasonings, and garnish with the Parmigiano croutons. Best served within 1 hour of finishing.