Rinse 1 cup of fresh mint leaves under cool running water and pat them completely dry with paper towels.

Cut 6 to 8 medium lemons in half and juice them using a citrus juicer or hand squeezer to yield 1 cup of fresh lemon juice.

Pour 1/2 cup granulated sugar into a large pitcher, add 1/2 cup cold water, and stir vigorously for 1 to 2 minutes until the sugar completely dissolves.

Add the prepared mint leaves to the sugar water and gently muddle with a wooden spoon or muddler for about 30 seconds to release aromatic oils.

Pour in the 1 cup of fresh lemon juice and add 1/8 teaspoon sea salt, then stir thoroughly for 30 seconds to combine.

Add the remaining 3.5 cups cold water to the pitcher and stir gently for 15 seconds, then taste and adjust sweetness or dilution as desired.

Strain the lemonade through a fine-mesh sieve into a clean pitcher or glasses to remove the mint leaves and any pulp.

Fill serving glasses with 1 to 2 cups of ice each, pour the strained lemonade over the ice, and garnish with fresh mint sprigs and lemon slices before serving.