I've had that a few times but the food was caught lower where I could still breathe, at least until enough saliva accumulated then I'd have to spit that out. Turned out I had a thing called a distal ring growing upstream of the esophageal sphincter (yes, we all have more than just that exit sphincter); this was apparently my body's natural reaction to heartburn. Anyways, on two separate occasions I had a hunk of steak poked the rest of the way in by a team in the ER. Not a pleasant routine but it sure beats the alternative!
One team later on was a Dr & nurse who were both rather easy on the eyes, they did a scheduled procedure to stretch that distal ring. I made a crack to my buddies afterwards that its the story of my life: There I was in a room with two hot women and a powerful sedative yet I was the one who woke up groggy & with a sore throat