Pour the coarse salt or celery salt onto a small plate. Run the lemon wedge around the rim of a highball glass, then dip the rim into the salt to coat evenly. Set the glass aside.

Fill the prepared glass with ice cubes and set aside while you make the drink.

Mix the Bloody Mary

In a cocktail shaker or mixing glass (no need to shake vigorously), add the vodka, tomato juice, fresh lemon juice, Worcestershire sauce, prepared horseradish, hot sauce, black pepper, celery salt, and smoked paprika if using.

Add 3–4 ice cubes to the shaker or mixing glass. Stir gently with a long spoon for about 15–20 seconds to chill and slightly dilute the mixture. (If you prefer a frothier, well-integrated drink, give a brief hard shake—10 seconds—but traditional Bloody Marys are usually stirred.)

Taste the mixture and adjust seasoning: add more hot sauce for heat, more Worcestershire for umami, or a little extra lemon juice for brightness. If it tastes too concentrated, add a splash more tomato juice.

Strain the mix into the prepared ice-filled glass.

Garnish and serve

Skewer the green olives on the cocktail pick and rest it across the top of the glass, or drop the olives into the drink if preferred.

Place the celery stalk into the glass as a stirrer and garnish. Attach the lemon wedge to the rim or drop it into the drink.

Serve immediately with a straw or long spoon. Encourage guests to stir before each sip to redistribute settled spices.