In the bowl of a stand mixer, beat the butter and peanut butter together until light and fluffy. In intervals, add both sugars until well combined. Add each egg, one at a time. Mix in vanilla.
In a separate bowl, combine the flour, baking soda, and salt. With the mixer running, add to the dough in intervals, until thoroughly combined, scraping down the bowl as necessary.
Preheat your oven to 350 degrees Fahrenheit. Roll the dough into golf ball-sized rounds and place on a prepared baking sheet, flattening slightly with your palm. Bake for 17-20 minutes, or until the edges are golden brown and the center is set. Let cool completely.
For the chocolate, place a heat proof glass bowl over the mouth of a sauce pan with 3″ of water inside (you don’t want the bowl to be touching the water). Pour the chocolate chips and coconut oil in the bowl, and turn the burner on medium heat. As the water starts to simmer, the chocolate will sweat and eventually melt. Don’t leave unattended, and continue to fold the chocolate over and scrape down the bowl until it and the coconut oil are thoroughly melted and combined.
Pour the melted chocolate into a narrow bowl (or a bowl big enough for you to dip a cookie in, but deep enough so half of the cookie can be immersed). Lay wax paper or foil on your prep area. Take one cookie and dip halfway into the chocolate, let drip so excess chocolate falls off. Lay on wax paper or foil, and sprinkle the chocolate half lightly with coarse sea salt.
Repeat with rest of cookies. Let set for four hours, up to overnight, or until the chocolate has hardened again.