For the polenta: Bring broth to a low boil. Slowly whisk in polenta until blended. Reduce heat and continue to stir until thickened, 3 to 5 minutes. Add butter, red pepper flakes and 1 teaspoon each salt and pepper. Stir. Add heavy cream and grated Parm. Stir.
Finely chop the roasted garlic and stir into the polenta. Season to taste with additional salt, broth and heavy cream. Set aside.
For the squid: Combine the olive oil, parsley, salt, pepper, red pepper, garlic, thyme, lemon juice and shallots in a food processor and process. Pour the marinade over the squid and toss well, then let stand at room temperature 10 to 15 minutes.
Transfer to a preheated grill pan and cook, turning occasionally, until tender with a slight char, 12 to 15 minutes. Toss with more lemon juice and salt, as desired.
For the carrots: Add the duck fat, garlic, shallot and thyme to a cast-iron skillet preheated over medium heat and let it all brown, stirring occasionally, about 7 minutes. Add carrots to the pan and add generous salt, pepper and red pepper flakes. Cook, stirring every few minutes, 8 to 10 minutes.
Deglaze the pan, a few teaspoons at a time, with the dry sherry. Continue to cook until tender, an additional 5 to 10 minutes, then add more salt and pepper to taste. Halve carrots lengthwise.
For the ghee Marsala sauce: Add the ghee, Marsala, parsley, red pepper, garlic, thyme and shallot to a saucepan and bring to a simmer. Simmer 8 to 10 minutes, then strain through a fine mesh strainer to get all large pieces out.
Spoon 1/2 cup polenta into each plate, followed by 6 to 8 pieces of squid each, about 3 pieces of carrot and 1 to 2 tablespoons ghee Marsala sauce.
This recipe was created by a contestant during a cooking competition. It has not been tested for home use.