In a bowl, with an electric mixer on medium speed, beat butter, 1/2 cup granulated sugar, and the brown sugar and peanut butter until very smooth. Beat in egg and vanilla until well blended, scraping down sides of bowl as needed.
In another bowl, mix flour, baking soda, and salt. Stir or beat into butter mixture until well blended.
Put remaining 1/4 cup granulated sugar in a shallow bowl. Shape dough into 1-inch balls, then roll in sugar to coat.
Place 1 1/2 inches apart on buttered or cooking parchment- lined 12- by 15-inch baking sheets.
Bake cookies in a 350 oven until slightly darker brown, 8 to 10 minutes; if baking more than one pan at a time, switch pan positions halfway through baking. Press a chocolate candy kiss into the center of each cookie (dough may crack). Continue to bake until chocolate is shiny and soft, about 3 minutes longer.
Using a wide spatula, transfer the cookies to racks to cool completely.
