Shake tequila, limeade, and peppermint schnapps together. Combine them in a cocktail shaker with ice, making sure the lid is secure before shaking vigorously. Shake until the shaker feels icy on the outside, which indicates that the mixture has chilled thoroughly and slightly diluted—an important step for smoothing out the strong spirits and allowing the peppermint to blend evenly with the citrus.
Pour over ice. Use fresh, clear ice if possible so the drink stays crisp without introducing off-flavors. Strain the mixture into a glass filled with ice to keep the texture clean and avoid adding shards from the shaker. The chilled mixture should appear bright and slightly opaque from the limeade.
Top with a splash of soda. Add just enough to introduce gentle bubbles and lift the aromatics without overwhelming the drink. The carbonation helps the peppermint aroma rise while keeping the lime profile refreshing. Stir lightly once or twice if needed to integrate the soda without losing too much effervescence.