Slice the ½ cup unsalted butter into pieces and melt it in a light-colored skillet over medium heat, stirring or whisking constantly. Once melted, the butter will begin to foam. Continue mixing/whisking for about 5-7 minutes; the butter will become a deep amber color. Remove the browned butter from the heat and pour it into a bowl. Allow the butter to cool for 30 minutes.
In a large bowl, add the browned butter, ¾ cup creamy peanut butter, ¾ cup brown sugar, and ¼ cup granulated white sugar. Whisk until there are no lumps of brown sugar.
Add the ½ cup sourdough discard, 2 egg yolks, and 2 teaspoons vanilla extract. Whisk together until smooth.
Stir in the 2 cups bread flour, 1 teaspoon baking soda, and ½ teaspoon kosher salt.
Wrap the dough in wax paper and refrigerate for at least 2-3 hours.
Preheat the oven to 350°F (180°C). Remove the dough from the refrigerator and roll it into balls, about 2 tablespoons of dough each.
Place the ¼ cup granulated white sugar into a bowl. Roll each ball in the sugar and arrange on baking sheets about 2 inches apart.
Bake for 10 to 12 minutes or until the edges are lightly browned but the center remains soft.
While the cookies are baking, unwrap the 30 - 40 Hershey Kisses.
Press a Hershey Kiss into the center of each cookie, then, using a thin spatula, immediately transfer the cookies to a wire cooling rack to cool completely.
Notes
Use a kitchen scale to weigh your ingredients rather than the cup measurements.Use room temperature butter, eggs, and sourdough discard. Chilled eggs or sourdough discard may cause some of the butter to re-solidify prematurely. To quickly bring the eggs to room temperature, place them in a bowl of warm water for 10-15 minutes.Chill the dough for at least 2-3 hours before baking. Chilling allows the butter to firm up and the flour to absorb more liquid further solidifying the dough. If the dough is baked without chilling it first, the cookies will spread while baking and become thin, hard, and crispy. Use a cookie scoop for evenly portioned cookies. Take the guesswork out of portioning cookies by using a cookie scoop to make sure each cookie is the same size. Alternatively, you could cut the block of cookie dough into even pieces with a knife. I find that this method saves me time.Baking times for all recipes are only suggestions. The actual baking time will vary depending on your oven.Storing: Baked cookies can be stored in an airtight container at room temperature for up to 4 days.