Make the salsa: Heat the oven to 400°F. Cut the tomatoes in half lengthwise and remove the seeds. Set them cut side down on a foil-lined baking sheet and cook until the skins split and the tomatoes soften, about 10 minutes. Let them cool slightly before removing their skins. Put the skinned tomatoes in the food processor with the remaining ingredients. Process until well blended. Adjust the seasonings and serve alongside the patties.
Make the turkey cakes: Put the diced turkey in a food processor and pulse until very finely chopped. Transfer to a bowl and add the cilantro, chives or scallion, chile, breadcrumbs, lime zest, lime juice, and gravy or cream; mix until well combined. Season with 3/4 tsp. salt and pepper to taste. Mix in the egg yolk.
With wet hands, mold the mixture into eight patties 1/2 inch thick; they should only just hold together. Cover with plastic and refrigerate for 30 minutes.
Put a baking sheet in the oven and heat the oven to 350°F. Put the cornmeal in a shallow bowl. Whisk the egg white with 1 tablespoon cold water. Dip the patties into the egg white and then coat with the cornmeal. Heat a large frying pan over medium heat; add the olive oil, and when it's hot, add the patties. Cook on each side until golden, about 2 minutes per side (work in batches if necessary). Transfer the patties to the heated baking sheet in the oven. Bake until heated through, about 5 minutes. Serve with the roasted tomato salsa.