To make the dough: In a large microwave-safe bowl, melt the peanut butter and butter in 20-second increments in the microwave. Whisk until well combined. (Alternatively, melt them in a saucepan over low heat on the stovetop, then transfer to a large bowl.)

Whisk in the sugars until no lumps remain, then whisk in the egg and vanilla, followed by the baking powder, baking soda, and salt.

Switch to a flexible spatula and stir in the flour until almost no dry streaks remain. Stir in the Jammy Bits.

Cover the bowl and transfer it to the refrigerator for 30 minutes to allow the cookie dough to firm up.

While the dough is chilling, preheat the oven to 350°F with a rack in the center, and line two baking sheets with parchment.

To prepare the coating: In a small bowl, combine the sugar and salt.

Using a 4 Tablespoon Scoop or a level ¼-cup measure, scoop the chilled dough into ten portions (about 75g each), coat each one in the sugar mixture, and divide evenly between the baking sheets.

Working with one pan at a time (leave the other baking sheet at room temperature), bake the cookies for 15 to 16 minutes, until puffy and soft in the centers and golden brown on the edges, then drop the tray firmly on the oven rack or countertop to deflate the cookies. (This helps create the crinkly surface.) Return the cookies to the oven for 1 to 2 minutes; the tops will still look soft. Remove from the oven and, once again, drop the tray firmly to encourage the cookies to deflate. Let the cookies cool completely on the baking sheet.

Bake the second pan of cookies. (Don't forget to bang the tray!)

Store the peanut butter and jelly cookies in an airtight container at room temperature for several days.