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Combine 1/2 cup of kosher salt with the Old Bay Seasoning on a pie plate and set aside.
Core the tomatoes and slice each into several wedges or chunks.
Lay a cooling rack inside a large rimmed baking sheet. Arrange the tomatoes in a single layer on the cooling rack. Lightly salt and pepper the tomatoes.
When ready to cook, start the Traeger grill on Smoke with the lid open until the fire is established (4 to 5 minutes).
Put the baking sheet with the tomatoes on the grill grate and close the lid. Smoke the tomatoes for 1 hour. Let cool.
Working in batches, liquefy the tomatoes in a blender or food processor, adding enough tomato juice to get the tomatoes moving. Transfer to a large bowl or pitcher. Strain if desired.
Stir in the lemon juice, Worcestershire, horseradish, onion powder, garlic powder, and celery salt. Taste for seasoning, adding more salt, pepper, lemon juice, hot sauce, horseradish, or spices as desired. The mix should be highly seasoned, but still taste of fresh tomatoes. Chill thoroughly in the refrigerator.
To make a Bloody Mary cocktail, rim a tall glass with the lemon or lime wedge. Dip the rim upside down in the salt/Old Bay mixture. Add ice cubes to the glass, then the vodka and olive brine, if using. Top with the tomato mixture and stir gently, being careful not to disturb the salted rim. Finish with your favorite garnishes.
Your choice of garnishes: homemade beef jerky or Slim Jim meat sticks; leafy celery sticks; pickled okra; dill pickles; pickled beans, onions, or asparagus; stuffed olives; peperoncini or other pickled peppers.