Wash the peaches thoroughly under cold running water.

Pit the peaches and slice them into thin wedges.

In a large pot, combine the sliced peaches, 4 cups water, 1 cup sugar, 1 teaspoon cinnamon, 1/2 teaspoon nutmeg, 1 tablespoon lemon juice, and 1/2 teaspoon vanilla extract.

Bring the mixture to a boil over medium-high heat.

Reduce heat to low, cover, and simmer for 30 minutes, stirring occasionally to prevent sticking.

Remove the pot from heat and strain the mixture through a strainer or cheesecloth into a clean pitcher, discarding the solids.

Allow the strained cider to cool to room temperature, about 15 minutes.

Transfer the cooled cider into a bottle or jar and refrigerate for at least 2 hours before serving. Serve chilled.