cold-shoulder

1816, in the figurative sense of "icy reception," first in Sir Walter Scott, probably originally a literal figure, but commonly used with a punning reference to "cold shoulder of mutton," considered a poor man's dish and thus, perhaps, something one would set out for an unwanted guest with deliberate intention to convey displeasure.

How often have we admired the poor knight, who, to avoid the snares of bribery and dependence, was found making a second dinner from a cold shoulder of mutton, above the most affluent courtier, who had sold himself to others for a splendid pension! ["No Fiction," 1820]

To “give someone the cold shoulder” is to ignore someone deliberately: “At the party, Carl tried to talk to Suzanne, but she gave him the cold shoulder.”

Deliberate coldness or disregard, a slight or snub. For example, When I said hello to her in the library, she gave me the cold shoulder and walked away. This term, which first appeared in writings by Sir Walter Scott and others, supposedly alludes to the custom of welcoming a desired guest with a meal of roasted meat, but serving only a cold shoulder of beef or lamb—a far inferior dish—to those who outstayed their welcome. [Early 1800s]