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.
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.
For the tomatoes, in a small bow, combine the parsley, breadcrumbs, parmesan, salt and pepper.
Slice the tomatoes in half lengthwise and remove the seeds. Arrange on a parchment paper-lined baking sheet and sprinkle with salt and pepper. Divide the filling between the tomatoes and roast for 12-15 minutes, until crisp and the cheese starts to brown slightly.
For the pesto, in a food processor, blend the basil, arugula, garlic, parmesan, olive oil, pine nuts, lemon juice, and salt and pepper until smooth. Adjust seasoning.
To serve, divide the mashed potatoes between plates. Top with chicken, roasted tomatoes, and pesto.