It is claimed he shouted: "You pay for your drinks, I'll pay for mine" and called her a "f***ing Spanish girl".
He then left the stall and began allegedly taking pictures of Ms Sanz on his mobile phone shouting "look how fat you are, you must be pregnant, how many babies do you have in there? At least three."
Prosecutor Edward Aydin said: "Mr Khan then started touching Ms Sanz's stomach.
"When her colleague, waiter Scott Gosnell tried to intervene, he said Khan allegedly shoved him in the chest and threatened to kill him."
He then shouted, "The Spanish are the weakest f***ers on earth", the court heard.
The court heard Khan continued to act in a threatening and abusive manner for over an hour while staff waited for police to arrive.
When he was arrested he told police officers "I only had two drinks, I didn't swear at anybody" before allegedly calling them "f***ing idiots".
Appearing via video link from Charing Cross police station, Khan denied one count of racially aggravated common assault in relation to Ms Katz, an alternative lesser charge of assault.
He also denied assaulting Mr Gosnell and obtaining services dishonestly in relation to the meal.
Listing the case for trial on June 13 at City of London Magistrates' Court, Magistrate Emma Stranack granted him bail on the condition he does not contact either Ms Sanz or Mr Gosnell or enter the Porter House restaurant.