Step 1In a large, heavy-bottomed saucepan, bring the chicken broth to a boil. Slowly rain in the polenta, whisking all the time. Once the broth has returned to a boil, reduce the heat to a simmer, add the herbs and cook, stirring frequently for 30 minutes. If the polenta gets thick or becomes difficult to stir, add more broth (or water) to loosen as necessary.
Step 2Meanwhile, heat a large saute pan over medium-low heat. Add one-third cup olive oil to the pan; when it's hot, add the onion. Season with salt and cook, stirring occasionally, until onion is translucent, 5 minutes.
Step 3While the onion is cooking, remove any bruised leaves from four heads of the radicchio and thinly slice each head crosswise down to its base, discarding the root end. Add the sliced radicchio, fennel and pepper to the onions. Reduce the heat to low, cover the pan and cook until the fennel is tender, about 20 minutes.
Step 4Add the mixture of fennel, onion and radicchio to the polenta. Season with salt to taste and continue cooking, stirring frequently, adding additional broth or water as necessary, until the polenta is tender to the tooth, an additional 20 to 30 minutes.
Step 5When the polenta is almost done, halve the three remaining heads of radicchio lengthwise. Brush each half with about one-half teaspoon olive oil and sprinkle with a pinch of salt and sugar. Grill, cut-side down, over medium-high heat for about a minute to soften the radicchio and caramelize the sugar. Set aside in a warm place.
Step 6Once the polenta is cooked, stir in the Parmigiano-Reggiano, season with Meyer lemon juice to taste, adjust seasoning as necessary. Serve the polenta in a pre-warmed pasta bowl, finishing with a grind of black pepper. Splay one of the grilled halves of Treviso radicchio over each bowl of polenta and serve immediately.