Preheat the grill to medium-high or use a grill pan.
Place the radicchio on a cutting board, and cut in quarters vertically, through the core. Drizzle cut sides with 1/2 Tbsp olive oil each. Grill the radicchio 1-2 minutes per side just to get a little char and smoke. Remove from grill and cut away the core. Slice radicchio into 1/2" slices, and transfer to a large bowl.
Add the cannellini beans, tuna, sun-dried tomatoes, and olives. Toss to combine, and set aside.
Add the lemon zest and juice to a small bowl. Stir in the capers, anchovy, shallots, red pepper flakes, olive oil, salt, and pepper. Whisk ingredients well, and pour dressing over the salad. Toss to combine.
Just before serving, chiffonade the basil by stacking the leaves on top of one another and rolling tightly into a cigar shape. Use a sharp knife to very thinly slice the basil crosswise into thin strips. Add the fresh basil to the salad, and toss to combine. Serve.