Because the Ottomans, Mughals, Qings, and Safavids had monopolies over the technical specialists and knowhow within their regions. In Europe, both France and the HRE had ownership or reign over regions where specialists and foundries popped up, so neither had an edge over the other. Additionally, the late middle ages saw some cooperation among european states against Muslim states, which meant an exchange or sharing of expertise.

However, you can see the disparity of specialists in combat between European powers who had more advanced foundries and other nations who had gunpowder but not the knowhow to develop larger cannons. One example of this is Portugal in India. There was plenty of gunpowder and cannons to go around, but the Portuguese used larger bronze cannons that deeply outranged the smaller and more precarious cannons of the coastal Indian kingdoms and rajas. A few Portuguese carracks with bronze cannons could (and did) fight forces magnitudes larger that still had cannons because theirs were larger/heavier hitting/longer ranged. Even against much larger ships -- like Chinese junkers -- the european bronze cannons prevailed. The only times that the Portuguese were really threatened was when they found enemies who had renegade Portuguese or Venetian help. (Sidenote: Venice helped the Mamelukes by tacitly allowing Venetian cannonmakers to make cannons to be used against the Portuguese in India, as Venice rightly knew that if Portugal was not stopped, then Venice's profitcenter of being the crossroads of the rich East and Europe would come to an end).

So in a way, there were large gunpowder empires in Europe -- they just projected outwards through colonialism rather than inwards (because none of them could capture a monopoly over the tech).