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 tablespoon 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.
I grilled the radicchio to get some smoky flavors into the salad - but it's not required for this recipe. If you'd prefer, just skip oiling and grilling the lettuce and slice it into 1/2" pieces. Continue with the recipe.