For the Stock:
Heat olive oil in large, heavy saucepan. Brown chicken well with garlic, thyme, and rosemary, about three minutes per side. Sprinkle with salt and pepper. Toss in diced vegetables and brown lightly, stirring once or twice, five to seven minutes. Pour prepared broth into pot, scraping bottom with wooden spoon to deglaze, add bay leaf, and bring to a simmer over high heat. Reduce heat to low and simmer 45 minutes to one hour. Pass stock through a fine strainer into large, clean saucepan. Set one of six cups total stock aside to finish sauce and bring remaining stock to a simmer.
While stock is cooking, peel and devein shrimp. Toss shrimp with lemon juice, salt, pepper, and herbs. Set aside. Meanwhile, heat oil in large skillet and cook pancetta until crisp and fat has rendered, about 10 minutes, adding garlic and herbs halfway through. Transfer pancetta and aromatics to plate in warm oven, leaving rendered fat in skillet. Remove skillet from heat—do not discard fat.
For the polenta:
Turn polenta into mixing bowl and whisk to a smooth slurry with two cups hot broth from saucepan. Return slurry to simmering stock, whisking vigorously. As soon as polenta bubbles around edges, whisk in cream, reduce heat to low, and cook, stirring occasionally, until polenta thickens to porridge consistency, about 10 minutes. Stir in olive oil. Set aside and keep warm.
Heat reserved pancetta fat in skillet over high heat. Add shrimp in single layer, and sear without turning, two minutes. Turn and sear second side, two minutes. Sprinkle flour over shrimp, turn shrimp, and sprinkle with lemon juice. Pour reserved broth into skillet, scraping with wooden spoon to deglaze. Bring to simmer and add butter, stirring to emulsify butter and thicken sauce. Remove skillet from heat, taste for seasoning, and sprinkle with parsley.
Spoon polenta into four shallow bowls. Sprinkle one tablespoon grated cheese over each. Arrange five shrimp per plate onto polenta and top with sauce. Garnish with reserved pancetta and herbs.