Preheat oven to 375 degrees and line 3 baking sheets with parchment paper. Set aside.

Cream shortening, peanut butter, and sugars together until light and fluffy, about 1-2 minutes. Add vanilla and eggs and mix until combined.

In a separate bowl, whisk together flour, baking soda, and salt and add to dough. Mix to combine. The dough will be very soft.

Using a 1/4 cup cookie scoop, scoop out the dough and roll it in the additional sugar. Place the dough on the cookie sheet and use a drinking glass with a flat bottom to flatten the cookie to about 1/2" thick. Repeat with remaining cookie dough--you should have 6 cookies on each baking sheet.

Bake for 9-13 minutes (this will vary depending on your oven and elevation; mine were perfect at exactly 11 minutes), until puffed and set and just barely beginning to brown around the edges. Remove from oven, let cool on baking sheet for 2-3 minutes and then transfer to cooling rack. Flip the parchment paper over so the clean side is facing up.

When the cookies are completely cool, combine the chocolate and oil or shortening in a bowl or mug wide enough to dip a cookie into. Melt the chocolate in the microwave for 30 seconds, stir, then place in the microwave for another 30 seconds and whisk until smooth (if the chocolate isn't completely melted and smooth, you can add a few seconds at a time until it's where you want it.) Dip half of the cookie in the chocolate and use a mini rubber spatula to spread it evenly (I actually find it easier to just spread the chocolate on from the get-go, but dipping it is kind of fun. Place the dipped cookies on the clean side of the parchment paper and allow to cool completely. Makes 18 cookies.