If you want a seasoned rim, run a lemon wedge around the glass lip to wet it. Combine celery salt and coarse salt or coarse pepper on a small plate. Dip the wet rim into the seasoning and twist to coat evenly. Set the glass aside.

Cocktail

Combine ingredients

Fill a cocktail shaker or mixing glass halfway with ice. Add 2 oz vodka, 4 oz bloody mary mix, 0.5 oz fresh lemon juice, 0.5 tsp Worcestershire sauce, 3 dashes hot sauce, 0.5 tsp prepared horseradish, 1 tsp freshly ground black pepper, and 0.25 tsp celery salt.

Mix

Cap the shaker and roll or gently shake once or twice to chill and integrate (10–15 seconds). Alternatively, stir briskly with a bar spoon for 10–15 seconds if using a mixing glass.

Assemble

Fill the prepared serving glass with fresh ice (about 1 cup). Strain the mixed Bloody Mary into the glass over the ice. Taste and adjust: add a dash more hot sauce for heat, a squeeze of lemon for brightness, or a pinch more celery salt if desired.

Garnish

Thread three pitted green olives onto a short cocktail pick. Place the olive pick across the glass or rest it inside. Add a lemon wedge on the rim and, if using, a celery stalk for stirring and aroma.