Hello and welcome to HCM,
what you are describing is called nasal regurgitation and its common especially after surgeries on the throat.
Many practitioners of yoga
can actually do what you described without much effort!!
If this is happening just once in a while then you have nothing to worry about, if it is happening often and its disturbing your diet in any way then consult an ENT.
Meanwhile do the following:
1. Maintain proper upright posture while swallowing and drink plenty of fluids while doing so
2. Do not try to blow your nose or try to bring out the food through the nose
3. Do not try to clean your nose without proper guidance as it is not necessary
Dr Sriram Nathan