In a cocktail shaker or mixing glass (no need to shake vigorously), add 2 oz vodka, 4 oz tomato juice, 0.5 oz fresh lemon juice, 1 tsp Worcestershire sauce, 0.5 tsp prepared horseradish, 3 dashes hot sauce, 0.25 tsp celery salt, about 6 grinds freshly ground black pepper, 0.125 tsp smoked paprika (if using), and 0.5 tsp olive brine (if using).

Combine and chill

Add 1 cup of ice to the shaker or mixing glass. Stir the mixture briskly for 20–30 seconds until well chilled and slightly diluted (stirring preserves the tomato juice texture; vigorous shaking can foam it). Taste and adjust seasoning: add more hot sauce for heat, more Worcestershire for umami, more lemon for brightness, or a pinch more celery salt if needed.

Prepare serving glass

Dump the chilling ice from the serving glass. Optionally, rim the glass with a lemon wedge and dip in celery salt or coarse salt for a seasoned rim.

Strain and serve

Fill the serving glass with fresh ice (if desired). Strain the mixed Bloody Mary into the glass over the ice.

Garnish

Garnish with a celery stalk and a lemon wedge on the rim. Add 1–2 cocktail olives on a pick if desired. Serve immediately.