Dressing
1/4 cup finely chopped fresh basil leaves
2 tablespoons white balsamic vinegar
2 tablespoons finely chopped shallot
Kosher salt
Freshly ground black pepper
Extra-virgin olive oil
Polenta
5 cups milk
1 cup water
1 1/2 cups quick-cooking polenta
4 ounces cream cheese, softened
1/2 cup grated Pecorino Romano cheese
1 ring fresh sweet luganiga sausage, about
1 pound, pierced a few times with a fork
3 fresh hot Italian sausages, about 8 ounces total
1 14-ounce package Polska kielbasa
Prepare the grill for indirect cooking over medium heat (350° to 450°F).
Whisk the dressing ingredients, including 1/2 teaspoon salt and 1/4 teaspoon pepper. Slowly add 1/2 cup oil, whisking constantly until the dressing is emulsified. Set aside.
In a saucepan combine the milk, water, 1 1/2 teaspoons salt, and 1/4 teaspoon pepper. Bring to a boil over medium-high heat, and then whisk in the polenta in a slow and steady stream. Reduce the heat to medium, and cook until the polenta is thick, 4 to 5 minutes, stirring constantly. Remove from the heat, and add the cream cheese and Romano cheese, stirring constantly until the cheeses are melted. Keep warm over low heat, stirring occasionally to prevent scorching.
Grill the luganiga and Italian sausages over indirect medium heat, with the lid closed, until fully cooked (160°F), 15 to 20 minutes, turning occasionally. At the same time, grill the kielbasa over indirect medium heat until nicely browned and heated through, 12 to 15 minutes, turning occasionally. If desired, during the last 3 to 5 minutes of grilling time, brown the luganiga and Italian sausages over direct heat, turning once. Remove all the sausages from the grill and cut them into bite-sized pieces.
Spread the polenta in a thick layer on a large serving platter. Top with the sausage pieces. Whisk the dressing again and spoon it over the sausages. Serve immediately.