Melt 4 tbsps. butter in a small saucepan over medium heat, to add to the cooked polenta. When it’s melted, remove it from the heat.
Heat 2 tbsps. oil in a large, heavy skillet over medium-high heat. Add the chicken breasts on the skin side, season with salt and pepper, and brown them only on their skin side, which will take about 5 minutes. If the chicken is browning too fast, turn down the heat to medium.
If the pan is crowded, brown the chicken in two batches.
When the chicken is browned, remove it from the pan.
Add the onions, the celery, and 1 tsp. red pepper flakes to the pan, stir, and season lightly with salt. Cook until the onions are soft, about 5 minutes.
Mince the parsley.
Add the crushed tomatoes to the onions, stir, then add the minced parsley and the rosemary sprigs and cook for 5 minutes.
Put the chicken breasts into the pan with the tomato sauce, along with any juices, pushing it down into the sauce. Bring the sauce to a simmer – you might have to increase the heat.
Make sure the sauce is at a steady simmer, cover the chicken, and cook for 20 minutes.
Whisk the polenta into the boiling, salted water in the large saucepan.
Keep whisking until the polenta thickens, and turn down the heat if it starts popping out of the pan at you. Cook and whisk the polenta for 5 minutes. Take the polenta off the stove and whisk in the melted butter and the ½ cup Parmigiano. Cover and forget about it for now.
Make the vinaigrette for the salad now: Put 1 tbsp. vinegar into a bowl, and whisk in a pinch of salt and 1 tsp. mustard.
Whisk in the shallot, then whisk in 1/4 cup olive oil. Taste it for seasoning. Put the lettuce leaves in the bowl, but DON’T TOSS THEM YET!
Set the table and check your Facebook and Twitter.
Check the chicken – it should be cooked all the way through. If it isn’t, leave it on the heat for another 5 minutes or so.
Transfer the polenta to a bowl, remove the bay leaf, and garnish with some herb sprigs.
Now you can toss, toss, toss the salad.
Remove the rosemary sprigs from the chicken and either serve it in the pan or transfer it to a large, shallow platter, and garnish with herb sprigs.
Get some help taking everything to the table. Don’t forget the wine!