Step 1

Place 1/2 cup freshly squeezed lemon juice in a blender. Add half of 1 (46- to 48-ounce) bottle or can tomato juice, 3/4 cup Worcestershire sauce, 1/2 cup prepared horseradish, 2 teaspoons hot sauce, 1 teaspoon celery seeds, and 1/4 teaspoon kosher salt. Blend on high until smooth, about 1 minute.

Step 2

Pour into an 8-cup or larger pitcher (or 10-cup pitcher if making a pitcher drink) and stir in the remaining tomato juice. Cover and refrigerate for at least 1 hour or ideally overnight. Meanwhile, refrigerate 2 cups vodka.

Step 3

Taste the bloody Mary mix and season with more kosher salt and more hot sauce as needed (or serve the hot sauce on the side).

Step 4

To serve individual Bloody Marys: Fill a Collins glass halfway with ice. Pour 2 ounces vodka over the ice. Top with about 6 ounces of the Bloody Mary mix and stir until just combined. Garnish with a celery stalk and pimento-stuffed olives and a lemon wedge speared with a toothpick.

Step 5

For a pitcher drink: Add all of the vodka to the pitcher and stir to combine. Pour into ice-filled glasses, stirring the drink before each pour (the tomato mixture and vodka may separate as they sit). Garnish each drink with a celery stalk and pimento-stuffed olives and a lemon wedge speared with a toothpick.