Pour 1 gallon of cold water into a large container.
Whisk in 3/4 cup of kosher salt and 1/2 cup of brown sugar until dissolved.
Optionally, add one tablespoon of uncrushed black peppercorns, 2 crumbled bay leaves, and 3 lightly crushed sprigs of fresh thyme.
Submerge one large skin-on turkey breast into the brine and refrigerate overnight.
After brining, pat the turkey breast dry with paper towels.
Place the turkey on a wire rack set over a foil-lined baking sheet.
Preheat your oven to 400°F.
Roast the turkey breast for about 30 minutes, or until it reaches a golden brown color and an internal temperature of 163°F.
Let the turkey rest until it reaches room temperature.
Wrap the turkey breast tightly in plastic wrap and refrigerate until completely cold, ideally overnight.
Slice the cold turkey breast thinly using a sharp knife.
In a medium bowl, combine 1/3 cup of mayonnaise, 1/4 cup of Dijon mustard, 1/4 cup of finely chopped parsley, and 2 grated cloves of garlic. Season with fresh ground black pepper and kosher salt to taste. Mix until thoroughly combined.
Heat a large skillet over medium-high heat with 3 tablespoons of vegetable oil until shimmering and hot.
Add 1/2 pound of grape tomatoes and let them sear, blister, and char.
Remove the tomatoes, season with salt and fresh cracked black pepper, and set aside.
Place thinly sliced onions in a bowl and rinse under running water for about 30 seconds to remove some of the abrasive qualities.
Slice 8 slices of sourdough bread for 4 servings.
Optionally, toast the bread in a toaster or in a pan with butter until golden brown.
Spread a generous amount of mustard mayo sauce on both halves of the bread.
Assemble the sandwich by adding lettuce, seared tomatoes, thinly sliced onions, and juicy turkey breast. Optionally, add 1 to 2 slices of Swiss cheese.
Top with the second slice of bread and serve immediately.