Make the peanut butter syrup: in a small saucepan combine 1 cup water and ¾ cup sugar. Whisk over medium heat until the sugar dissolves.
Whisk in ¾ cup peanut butter until fully combined. Let the mixture come to a gentle simmer and bubble for 3 to 4 minutes, whisking often.
Remove the saucepan from the heat and stir in ½ teaspoon vanilla extract. Let the syrup cool completely to room temperature. Transfer to a jar or bottle and refrigerate; it will keep about one week.
To assemble one latte, pour 2 ounces peanut butter syrup into a glass. (Use more than 2 ounces if you prefer it sweeter or more peanut-butter-forward.)
Add 2 shots freshly brewed espresso to the glass and stir until the syrup is dissolved into the espresso.
Pour 6 to 8 ounces milk into the glass and stir or shake to combine.
If desired, drizzle additional peanut butter syrup on top for garnish and serve.