1) Whisk the flour, baking soda, and salt together. Set aside.
2) Using a hand mixer or a stand mixer fitted with paddle attachment, beat the butter for 1 minute on high speed until creamy. On medium-high speed, beat in 1/4 cup of granulated sugar and the 1/2 cup of brown sugar until completely creamed and smooth, about 2 minutes. Add the egg and beat on high until combined, about 1 minute. Scrape down the sides and bottom of the bowl as needed. Add the peanut butter and vanilla extract and mix on high until combined.
3) Add the dry ingredients to the wet ingredients and mix on low until combined. Cover and chill the dough for at least 30 minutes in the refrigerator (and up to 1 day). If chilling for longer than a few hours, though, allow to sit at room temperature for at least 30 minutes before rolling and baking because the dough will be quite hard and the cookies may not spread much
4) Preheat oven to 350°F (177°C). Line two large baking sheets with parchment paper or silicone baking mats. (Always recommended for cookies.) Set aside. Also, make sure there is room in your freezer because they will later need to be placed inside to prevent the Kisses from melting on the warm cookies.
5) Scoop and roll cookie dough, about 1 Tablespoon of dough each. Roll each ball in the remaining 1/2 cup of sugar and arrange on the baking sheet about 2 inches apart. Bake for 10 minutes or until the tops begin to slightly crack. Remove cookies from the oven and allow to cool for 10 minutes.
6) Press a chocolate kiss candy into each cookie on 1 of the baking sheets until it sticks. Place the baking sheet in the freezer so the chocolate does not melt. Remove after 10 minutes in the freezer. Repeat with 2nd baking sheet of cookies.
7) Make ahead tip: Cookies stay fresh covered at room temperature for up to 1 week. You can make the cookie dough and chill it in the refrigerator for up to 1 day. Allow to come to room temperature then continue with step 4. Baked cookies freeze well for up to 3 months. Unbaked cookie dough balls freeze well for up to 3 months. Bake frozen cookie dough balls for an extra minute, no need to thaw.