Adjust oven rack to middle position and heat oven to 350°.
Line 12 cup muffin tin with paper or foil liners.
Place chocolate and cocoa in medium heatproof bowl.
Heat the beer to boil in a small saucepan. Once hot, pour over mixture and let sit, covered for five minutes.
Whisk mixture until smooth, then transfer to refrigerator to cool completely. About 30 minutes.
Whisk flour, sugar, salt, pumpkin pie spice, nutmeg and baking soda together in a medium bowl.
Whisk oil, eggs, vinegar, pumpkin puree and vanilla into cooled chocolate until smooth.
Add flour mixture and whisk until smooth.
Using an ice cream scoop, divide batter evenly among prepared muffin cups. Place 1 slightly rounded teaspoon ganache on top of each portion of batter.
Bake cupcakes until set and just firm to touch, 18 to 20 minutes, rotating muffin tin halfway through baking.
Let cupcakes cool in muffin tin on wire rack for 10 minutes. Remove from tin and let cool completely on a wire rack, about 2 hours.
Once cool, pipe remaining ganache into the cupcakes.