Preheat your oven to 350. Either line a muffin tin with cupcake liners or grease and flour the tin.
Make your flax egg and set it aside.
In a mixing bowl, either with your stand mixer or hand mixer. Mix the brown sugar, peanut butter, and oil. Mix this until it's fluffy.
Now add the flax eggs and the vanilla, baking powder, cream of tartar, and salt. Mix.
Add your flour and milk alternately until they are both all mixed in. Now mix in your chopped peanut butter cups. Fill your muffin tin; I use a big scoop to make sure they are even. Bake for 15-20 minutes. Start checking for a clean toothpick at 15 minutes. You don't want to overbake them. Let them sit for about 5 minutes in the muffin tin, then place them on a cooling rack.
While your cupcakes are cooking, you can make the Ganache. Place all the ingredients into a glass bowl and microwave for 30 seconds, stir, stir, stir, do another 30 seconds, and at that point, it should be ready after a lot of stirring. If you still have a lot of solid chunks, then microwave at 50% power at 15-second intervals; you don't want your chocolate to seize up. Stir until no solid pieces, it may be a bit grainy, but that's okay. Put in the fridge until your cupcakes are cool enough to fill.
While waiting, you can make your frosting. Take a clean mixing bowl, and mix your peanut butter and butter until creamed. Add the rest of the ingredients, but add the powdered sugar one cup at a time on low speed ( so you don't have a powder sugar dusting in your kitchen). Once all is mixed, add your chopped peanut butter cups. Set aside.
Once your cupcakes are cooled, you can start filling them. I use this, and it is THE best for filling; I have tried many different things. But if you don't have one- you could use a piping bag and pipe them into your cupcakes. If you don't have piping bags, you'll have to get creative- a zip lock bag would work, with a corner cut out, but it will get messy (this is not my recommended way, but you have to do what you have to do). I fill the cupcakes with about 1.5 MLS, don't overfill because your cupcake will explode. Once they are all filled- you can top them with frosting.
I use a medium cookie scoop and scoop a ball out, flatten it in my hand, and add it to the top of the cupcakes. Top with a little peanut butter cup, and enjoy your hard work!