Mix the instant coffee with brewed coffee in a small bowl and set aside. Chop the chocolate and add to a microwave safe bowl with the coconut oil. Melt at 40% power, stirring every 30 seconds, until the chocolate has fully melted. Set aside to cool. Alternately the chocolate and coconut oil can be melted using a double boiler.
In the bowl of a stand mixer with the paddle attachment, add the cream cheese and stir until all of the lumps are gone. Scrape the bowl, then stir again. Stir in the powdered sweetener, scrape the bowl, then mix in the sour cream and eggs, one at a time, stirring after each addition. Do the same with the vanilla, then mix in the instant coffee / cold coffee mixture. Be sure to scrape all the way down to the bottom of the bowl in between each addition.
Remove 1 cup coffee cheesecake batter. Stir the melted chocolate into the removed coffee batter to create mocha cheesecake batter! Pour the remaining coffee cheesecake batter into the prepared springform pan, overtop of the chocolate crust.
Scrape the mocha cheesecake batter into a piping bag and squeeze out the entire contents into the coffee cheesecake, all over, in little dollops inside the cheesecake and on top, until all of the mocha cheesecake batter is used up.
Take a knife or chopstick and swirl it back and forth through the blobs of mocha cheesecake batter, to create a beautiful swirl design, then place the cheesecake inside a baking dish and bring a kettle of water to boil.
Pour boiling water inside the baking dish, until it comes about 1" up the side of the springform pan. Make sure it will not reach the lowest side of the tin foil - we don't want the water to get into the tin foil and sogg-y-fy the cheesecake!