Preheat your oven to 375 degrees Fahrenheit and line two large baking sheets with parchment paper.
In a medium bowl, combine 1 cup granulated sugar, the peanut butter, egg, vanilla extract, baking soda, and salt. Mix with a sturdy spoon until a uniform, slightly crumbly dough forms.
Shape the dough into 1-inch balls, then roll each ball in the reserved ½ cup of granulated sugar to coat it completely.
Place the sugar-coated dough balls about 2 inches apart on the prepared baking sheets.
Bake for 8 to 10 minutes, or until the cookies are lightly browned and the surfaces are crackled.
Immediately upon removing the baking sheets from the oven, firmly press one unwrapped chocolate kiss into the center of each hot cookie. The cookie will form a slight crater around the candy.
Let the cookies cool on the baking sheets for 5 minutes before transferring them to a wire rack to cool completely, which will allow the chocolate to set.