Grilled Bloody Mary

Light a grill and set it up for direct heat or preheat a grill pan. Brush the grill grates with oil and arrange the tomatoes and lemons cut side down and grill over high heat until well browned on the bottoms, 4 to 5 minutes. Grill 3 of the celery stalks, turning occasionally, until the leaves are dark brown or black and the stalks are blistered in spots, 5 to 6 minutes. Grill the remaining 4 celery stalks just until the leaves are singed, about 1 minute.
Transfer the tomatoes and fully grilled celery stalks to a food processor and let cool slightly. Squeeze 3 tablespoons of juice from the lemons and add it to the food processor; reserve the lemons. Add the Worcestershire, horseradish, sugar, 1 ½ teaspoons of salt and ½ teaspoon black pepper to the processor and process until as smooth as possible.
Strain the Bloody Mary mix through a fine sieve into a liquid measuring cup, pressing on the solids; you should have at least 2 cups of mix. Season the mix with more lemon juice, salt and pepper, if desired.
For each drink: In an ice-filled cocktail shaker, combine ½ cup Bloody Mary mix with 2 ounces of vodka; close and shake well. Pour the Bloody Mary into a tall ice-filled, garnish with a singed celery stalk and serve with Tabasco or Sriracha, for seasoning. Fill the cocktail shaker with clean ice before making each drink.