Line a small serving glass with fresh lime juice and dip in coarse salt (optional).
Add tequila, lime juice, ginger beer, simple syrup, and ice to a large glass or cocktail shaker and stir vigorously. Don't shake with a lid on or it will erupt from the ginger beer carbonation (lesson learned).
Pour liquid (reserving ice) into serving glass with a few ice cubes (we just ordered this oversized ice cube mold and LOVE it). Garnish with a lime wedge and serve immediately. Repeat for more drinks, or double/triple the amounts for more people.