Run the lemon wedge around the rim of a highball or pint glass. Dip the rim into a shallow dish with the kosher or celery salt to coat. Add ice to the glass to chill while you mix the drink.

Mix ingredients

In a cocktail shaker or mixing glass filled with a few ice cubes, combine 2 oz vodka, 4 oz tomato juice, 0.5 oz fresh lemon juice, 0.5 tsp Worcestershire sauce, 3 dashes hot sauce, 0.5 tsp prepared horseradish, 0.25 tsp celery salt, 6 grinds freshly ground black pepper, 0.125 tsp smoked paprika (if using), and 0.5 tsp pickle or olive brine (if using).

Shake or stir

If you prefer a slightly frothy, well integrated drink, give the shaker a short, gentle shake (about 5–7 seconds). For a smoother, less aerated result, stir vigorously with a bar spoon for about 15 seconds. Both methods chill and dilute slightly.

Assemble

Discard the ice used to chill the glass, then fill the prepared glass with fresh ice. Strain the mixed Bloody Mary into the glass over the ice. Taste and adjust seasoning: add more hot sauce for heat, more lemon for brightness, or a pinch more celery salt for savory depth.

Garnish

Skewer the olives and optional pickled vegetables on a cocktail pick. Add the celery stalk and the skewer to the glass. Finish with the lemon wedge on the rim or placed in the drink. Serve immediately with a long spoon or straw.