Preheat the oven to 450° F.
Bring the water to a slight boil in a medium saucepan. Slowly stir in the polenta in a steady stream to prevent clumping. Continue stirring until the cornmeal thickens slightly, 1-2 minutes.
Reduce the heat to a simmer, stir in the cheese, and season with salt. Stir until the mixture is thick but still pourable, about 2 minutes.
Pour the polenta into a lightly oiled 8 X 8 baking pan and tilt it back and forth to create a smooth, even layer. Bake uncovered until barely golden on the outside and still creamy on the inside, 30 minutes. Remove and let cool 5 minutes before slicing.
To make the sauce, place the garlic, 1/2 teaspoon of salt, and red pepper flakes in a shallow bowl. With the back of a fork, mash the ingredients together until the garlic is pasty. Add 1 tablespoon of oil and continue mashing until well blended.
Heat a medium skillet or saucepan over medium-low heat and add the garlic mixture. Cook 1 minute, stirring frequently, until very aromatic. Add the tomato paste and 2 tablespoons of oil to the skillet and stir 1 minute.
Add the vegetable broth and bring to a simmer. Reduce the heat and simmer slowly 5 minutes. Cover and keep warm while the chicken cooks.
To prepare the chicken, combine the flour, paprika, salt, and pepper in a large, zip-top bag. Add the chicken and shake to coat well.
Heat a large, nonstick skillet over medium-high heat and add 2 tablespoons of oil. Shake any excess flour from the chicken strips and add to the skillet. (Season with additional salt and pepper, if desired.)
Fry 4 minutes on 1 side, then turn and fry 3 minutes on the other side, until golden and just cooked through. Remove to a plate and let rest while the zucchini cooks.
Add the zucchini rounds to the drippings in the skillet and sear, stirring frequently, until crisp-tender, 3-4 minutes.
To serve, cut the polenta into 4 large squares (or 6 slices and save 2 for leftovers) and divide among plates. Lay 2 chicken strips over each and divide the zucchini among them. Spoon the tomato sauce over the chicken and polenta and serve right away.