BLACK smoke would be improper combustion. BLUE smoke COULD be valve cover. OP said black smoke.
OP, My guess is, with e combo of black smoke and hesitation, you're getting bad misfires. I would check your plugs and see what they look like. Ignore the bozos who are saying its your valve cover, they're confused.
If I were in your shoes and I didn't know the age of my plugs or coil packs, I would just buy all new both. Good OEM Bosch (FR6KPP332S) or NGK plugs (BKR7EIX) run about $8 each and good OEM coil packs (p/n: 07K905715F) run about $20. Keep in mind that the proper heat range for the 2.0t is NGK-7 or Bosch-6. Don't let anyone tell you otherwise. Older 1.8t engines used to have a NGK-6 heat range stock and its a VERY common misconception in this forum that the 2.0t shares this. the 2.0t is one range colder stock.
Hope some of this info helps
Edit: Just saw you said you changed plugs 10k miles ago. What plugs did you use? If you used copper based plugs (bkr7e or bkr6e) then those plugs have reached the end of their service life and should be replaced anyway.
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