Combine 1 cup water and 1 cup granulated sugar in a small saucepan. Add 2 oz (about 50 g) thinly sliced peeled fresh ginger. Bring to a gentle simmer over medium heat, stirring until sugar dissolves. Reduce heat and simmer 8–10 minutes to infuse ginger flavor. Remove from heat and let cool to room temperature, steeping at least 30 minutes for stronger ginger. Strain syrup through a fine mesh sieve, pressing on solids to extract liquid. Stir in 1 teaspoon fresh lemon juice if using. Transfer syrup to a jar and refrigerate. Yields roughly 6 oz; syrup keeps 2 weeks refrigerated.

Cocktail Assembly

Build and shake

Fill a cocktail shaker half to three-quarters with ice. Add 1.5 oz peach tea Smirnoff (or peach-flavored vodka), 0.75 oz simple syrup (substitute peach simple syrup if you have it), 0.5 oz peach schnapps, 0.75 oz fresh lemon juice, and 0.5 oz house-made ginger syrup. Secure the lid and shake vigorously for 10–15 seconds until well chilled and slightly diluted.

Finish

Fill a Collins glass (or an 8–12 oz highball glass) with fresh ice. Strain the shaken cocktail into the glass. Top with 2 oz cold water or club soda if you prefer a longer, lighter lemonade-style drink; gently stir once to combine.

Garnish and serve

Garnish with a lemon wheel on the rim and an optional mint sprig. Serve with a straw. Taste and adjust sweetness: add an extra 0.25–0.5 oz simple syrup if you want it sweeter, or a splash more lemon juice if you prefer brighter acidity.