Combine celery salt and coarse salt on a small shallow plate. Rub the lemon wedge around the rim of a highball or pint glass to moisten, then dip the rim into the salt mixture to coat. Set the glass aside.

Cocktail

Chill glass

If desired, fill the prepared glass with ice to chill while you mix the cocktail, then discard or keep the ice as preferred.

Mix

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

Combine with ice

Fill the shaker or mixing glass with ice (about 1 cup). Stir the mixture briskly for 15–20 seconds to chill and lightly dilute the drink. If you prefer a more aerated texture, give it a gentle roll or 5–6 short shakes and then stir once to integrate.

Taste and adjust

Taste a small sip and adjust seasoning to your preference: add more hot sauce for heat, more Worcestershire for umami, extra lemon for brightness, or additional horseradish for bite. Stir briefly after any adjustments.

Serve

If you chilled the serving glass with ice, discard that ice and strain the cocktail into the prepared glass filled with fresh ice. Otherwise, pour over fresh ice in your glass.

Garnish

Garnish with a celery stalk, a lemon wedge on the rim, and 1–2 cocktail olives or a pickle spear. Optionally, add other skewered garnishes like a cherry tomato or cooked shrimp for a more elaborate presentation.