Start by pouring 1 cup of water into a small saucepan and add the granulated sugar. Heat the mixture over medium heat until the sugar dissolves. This should take about 3-5 minutes. Once dissolved, remove from heat and let it cool completely.

While your simple syrup is cooling, take fresh lemons and cut them in half. Use a citrus juicer to extract the juice until you have a full cup. Strain through a fine-mesh sieve if desired to remove seeds or pulp.

In a large pitcher, combine the cooled simple syrup, freshly squeezed lemon juice, and 4 cups of cold water. Stir gently for about 30 seconds to mix well.

Cover the pitcher with plastic wrap and place it in the refrigerator to chill for at least 1 hour.

When ready to serve, fill tall glasses with ice cubes and pour chilled lemonade over the ice. Garnish with lemon slices and mint sprigs if desired.