Butter a 9x9 inch baking pan and set aside.
In a heavy saucepan, combine the minced garlic, red pepper flakes and chicken broth. Bring to a boil, then whisk in the polenta. Continue whisking and reduce heat, cooking mixture until thickened and grains have become tender, about 7-10 minutes.
As soon as polenta is done, mix in green onion and Parmesan, then season to taste with salt and pepper. Quickly pour polenta into the prepared baking pan and spread with a spatula to smooth the top. Cover with plastic wrap and place in the refrigerator until cool and firm, anywhere from 30-60 minutes; cut into squares, diamonds or circles.
While polenta is cooling, blanch each vegetable separately in boiling water, immersing each batch in ice water and draining afterwards. Set aside.
In a nonstick skillet, add enough equal parts olive oil and butter to generously cover bottom of pan. Place over medium-high heat until hot but not smoking. Sauté the polenta pieces browning lightly, about 2-3 minutes per side. Set on a paper towel to drain.
Pat veggies dry, then quickly sauté them in the same pan as the polenta, adding a bit more oil, if necessary. Serve hot vegetables over polenta and garnish with extra Parmesan cheese. Sprinkle with salt and freshly ground black pepper, to taste.