Preheat the oven to 350°F (177°C). Line two large baking sheets with parchment paper or silicone baking mats and set aside.
In a large mixing bowl, whisk together the flour, baking soda, and salt. Set aside.
In the bowl of a stand mixer fitted with the paddle attachment, or in a large mixing bowl using an electric mixer, cream together the butter, brown sugar, and granulated sugar for 1-2 minutes or until well combined.
Mix in the peanut butter, egg, and vanilla extract until fully combined, stopping to scrape down the sides of the bowl as needed. Mix in the dry ingredients until just combined.
Place the 3 tablespoons of granulated sugar in a small bowl. Using a 1.5 tablespoon cookie scoop, scoop the dough from the bowl, roll into a ball, and roll in the granulated sugar. Place each ball of cookie dough on the prepared baking sheets, making sure to leave a little room between them.
Bake in separate batches at 350°F (177°C) for 10-12 minutes or until the tops of the cookies are set. Remove from the oven and gently press a chocolate kiss candy in the center of each cookie. Allow to cool on the baking sheet for 5-10 minutes, then carefully transfer to a wire rack to cool completely.