Heat the oil in a medium saucepan over medium heat. Add the onion, carrot and celery and cook until soft. Add the garlic and cook 1 minute. Increase the heat to high. Add the red wine and port and cook until reduced by three-quarters. Add the stock and cook until reduced to 2 cups. Strain the sauce into a bowl and add the piquillo peppers and, cracked pepper and season with salt.
Preheat oven to 450 degrees F. Heat butter and oil in a large saute pan over medium high heat. Season the squab with salt and pepper to taste and place in the pan, breast side down and cook until golden brown. Turn the squab over, place in the oven and roast for 10 to 12 minutes. Remove from the oven and let rest 5 minutes.
Heat olive oil in a medium saucepan over medium heat. Add the onions and garlic and cook until soft. Add the cumin and cook for 2 minutes. Increase the heat to high, add the water and 1 tablespoon of salt and bring to a boil. Whisk in the yellow cornmeal, reduce the heat to low and cook for 20 to 25 minutes, stirring with a wooden spoon occasionally until the mixture pulls away from the pan. Add the chickpea puree and cook for 5 minutes. Place the mixture into a buttered 8 by 10 baking dish and refrigerate until firm, about 2 hours. When ready to serve, heat the butter in a large skillet over medium heat. Cut the polenta into 2-inch squares or circles, season with salt and pepper and saute on both sides until golden brown. Garnish with parsley and serve with the squab and pepper sauce.