Preheat oven to 350º. Line one or two baking sheets with parchment paper or a baking mat. To bake one tray at a time, position the oven rack in the center of the oven; for two, position the racks in the upper and lower thirds.

In a large mixing bowl, whisk together the brown sugar and eggs until smooth. Mix in the vanilla, then the peanut butter, and whisk until all of the ingredients are fully incorporated and no streaks of peanut butter remain. 

Scoop or spoon the dough into balls and place on the prepared baking sheets about 2 inches apart. I use a #30 scoop which holds a little over 2 tablespoons. Sprinkle the tops with some coarse sea salt or kosher salt. Bake the cookies for 18-20 minutes, rotating the pans halfway through baking time if using two racks. The cookies will be golden at the edges when done. (If you use a larger or smaller scoop size, adjust the baking time accordingly.) Let the cookies cool on the sheet for a couple of minutes and then transfer to a cooling rack. Let cool completely.

Line a baking sheet with wax paper. Place the chopped chocolate in a small bowl or mug with an opening large enough to dip the cookies. Melt the chocolate in the microwave for 30 second intervals, stirring between each interval, until only a few small pieces of chocolate remain. Continue stirring until the chocolate is smooth and completely melted. (Be careful not to scorch the chocolate!) Partially dip each cookie in the melted chocolate letting any excess drip back into the bowl and then place on the wax paper lined sheet pan. Sprinkle with a little more coarse salt if desired. Once all of the cookies have been dipped, place them in the refrigerator for a few minutes until the chocolate is set.