If you have leftover chicken, especially grilled chicken, this would be a great way to use it. Otherwise, if cooking chicken just for this purpose seems like too much bother, skip it or throw in some chickpeas instead.
To do this properly, prepare the polenta ahead of time so it has time to chill and solidify in the refrigerator. If you don't plan that far ahead, though, you can serve it soft in bowls and spoon the topping over it for an equally delicious result. I usually make polenta in my rice cooker now - no fuss, no stirring, no getting burned by spattering polenta - but I've given stovetop instructions below.
4 1/2 cups water
1 cup coarse cornmeal
1/2 cup quinoa (or another 1/2 cup cornmeal)
1 1/2 tsp salt
1 medium onion, sliced lengthwide
1 medium summer squash, diced
1 cup sliced shiitake mushrooms
3-4 cups diced cooked chicken
3 cups tomato sauce
Salt and pepper to taste
Crumbled feta for topping
Prepare the polenta: Bring the water to a boil. Whisk in the cornmeal, then add the quinoa and salt. Return to a boil, then reduce heat to low and simmer, stirring frequently, until it reaches the desired consistency (it should be quite thick). Oil a 9x13-inch pan and spread the polenta into it in an even layer. Cover with plastic wrap and let cool. Refrigerate when no longer hot.
When you are ready to prepare the meal, slice the polenta into squares. Spread them on a baking sheet and broil for 5-10 minutes, until crispy on the outside and beginning to brown.
Prepare the vegetables: Heat a little olive oil in a large skillet. Add the onion, squash, and shiitakes and saute until tender, about 5 minutes.
Prepare the sauce: Combine the chicken and tomato sauce in a saucepan and heat through.
To serve the dish, place squares of broiled polenta on plates. Top with a spoonful of vegetables followed by a spoonful of sauce (alternatively, stir the vegetables into the sauce). Top with crumbled feta at the table.