Combine the lemon, parsley, garlic, oil and salt in a blender until mostly smooth.
Toss the chicken with the gremolata and marinate overnight or for at least 4 hours.
Preheat the oven to 350°F.
In a large skillet, add the canola oil and butter. When the butter melts, stir in the flour and cook for 15-20 minutes, until golden and thick. Add the onions, salt and pepper and cook until soft, about 7 minutes. Add the sherry vinegar and marsala and bring to a boil. Add the chicken stock and mushrooms and return to a boil. Reduce to a simmer and cook for 15-20 minutes, until flavorful and thickened. Season to taste.
Remove the chicken from the marinade, discard marinade and season chicken with salt and pepper. Roast on a baking sheet until cooked through, about 22 minutes.
In a large stockpot, place the potatoes and a generous pinch of salt. Cover with cold water and bring to a simmer. Cook at a simmer until the potatoes are fork-tender, about 15 minutes. Drain the potatoes and return to the pot. Add the butter, milk, buttermilk, salt and pepper. Mash until smooth. Fold in the scallions.
Bring a large pot of salted water to a boil for the broccoli. Prepare an ice bath by filling a large bowl with water and ice. When the water boils, add the broccoli for 2 to 4 minutes, until bright green, then immediately transfer to the ice bath to stop cooking. Take them out of the ice bath after 1 to 2 minutes.
To serve, divide the mashed potatoes and broccoli between plates. Top with a chicken breast and marsala sauce.