Run the lemon wedge around the rim of a highball or pint glass. Spread the kosher salt or celery salt on a small plate, then dip the wet rim into the salt to coat evenly. Set the glass aside.

Fill the prepared glass with ice (large cubes or a full ice fill) and set aside while you mix the cocktail.

Mix the Cocktail

Combine base ingredients

In a cocktail shaker (or mixing glass) add vodka or tequila (2 oz), tomato juice (4 oz), fresh lemon juice (0.5 oz), Worcestershire sauce (2 tsp), prepared horseradish (0.5 tsp), hot sauce (3 dashes), celery salt (1 tsp) and freshly ground black pepper (4 grinds). If using any optional add-ins, add them now (for example substitute Clamato for tomato juice or add 1 tsp smoked hot sauce).

Stir (do not shake)

Add a handful of ice to the shaker or mixing glass and stir for about 15–20 seconds until the mixture is well chilled and slightly diluted. Bloody Marys are traditionally stirred (not vigorously shaken) to maintain texture.

Taste and adjust

Taste a small amount (or pour a little over ice from the mixing glass) and adjust seasoning to your preference: more hot sauce for heat, more Worcestershire for depth, more lemon for brightness, or a pinch more celery salt. If it's too thick, add a splash (0.25–0.5 oz) of tomato juice or a few drops of water.

Strain and serve

Strain the chilled mixture into the prepared ice-filled glass. If you prefer a chunkier garnish, you can pour directly without fine straining.

Garnish

Skewer the olives, cherry tomato and pickle spear on a cocktail pick and rest it across the rim, or stand the celery stalk in the drink for a classic presentation.

Squeeze the remaining lemon wedge over the drink if desired and drop it in as additional garnish.

Serve immediately with a long spoon or straw and an optional small plate for garnishes.