1. In a medium bowl, mix the ricotta with the mozzarella. Season with salt and pepper.
2. In a large bowl, mix the anchovies with the 3 tablespoons of olive oil, lemon juice and garlic. Season with salt and pepper.
3. Oil 3 large baking sheets. Cut the pizza dough into 6 equal pieces and pat into disks. On a lightly floured surface, roll each disk into an 8-inch round and dust with flour. Place 2 rounds on each baking sheet and let stand in a draft-free place until they begin to rise, about 20 minutes.
4. Light a grill. If using a gas grill, set the center burner on high heat and the front and back or side burners on low. Brush the dough generously with olive oil. Using your hands, stretch each piece out into a 9-inch round, lifting the dough as necessary.
5. Working with 1 piece of dough at a time, quickly lift it off the baking sheet and drape it over the center of the grill; use long-handled tongs to straighten out any folds. Grill the dough over a hot fire for 10 seconds, then slide it over to a low fire and grill until lightly charred on the bottom, about 10 seconds longer. Flip the pizza and spread a scant 1/2 cup of the cheeses over half of it. Rotate the pizza over the hot and cooler areas of the grill to finish cooking the dough and heat the cheese, about 40 seconds. Transfer the pizza to a plate.
6. Add the tomatoes and radicchio to the anchovy dressing and toss. Spoon a rounded 1/2 cup of the radicchio salad over the cheese and fold the other half of the crust over the filling, cut in half and serve at once. Repeat with the remaining dough and fillings.
Wine Recommendation: A light, fruity Italian red with good acidity will contrast the richness of the cheese and blend with the acidity and bitterness of the salad. Opt for a juicy Valpolicella Classico, such as the 1999 Allegrini or the 1999 Bertani.