The ice cream company urged Ms Braverman to not only "scrap the Rwanda plan" but also to "take dessert breaks".
Ben & Jerry's tweeted a message of congratulations to Ms Braverman alongside an image of a list including various objectives for the former Attorney General.
The list included potential policies such as lifting "the ban" and giving "people seeking asylum the right to work” while also introducing "safe routes to the UK for people seeking asylum”.
The company also included a coffee and ice cream break in the list.
Ben & Jerry's issued a to-do list to Suella Braverman
Wiki Commons
Suella Braverman arrives at Number 10
TOBY MELVILLE
But the post did not go down well.
In response, the Campaign For Common Sense created a "to-do list" for Ben & Jerry's.
Their post included "stick to selling ice cream" and "stop trying to distract from the fact you're owned by a massive multinational called Unilever that exploits poor countries".
It comes as Ms Braverman is expected to ask the French for joint beach patrols to help prevent Channel migrant crossings, after making her first speech to Home Office staff on Wednesday.
A decision over extending last year’s £54million agreement was put on hold over the summer until a new Prime Minister and Home Secretary were installed.
She told staff that tackling the Channel migrant crisis was going to be one of her "clear priorities" as she told them she was going to "develop some obsessions".
Ms Braverman added: "This is not just a manifesto pledge, people are dying."
Both Ms Braverman and Prime Minister Liz Truss are committed to the Rwanda asylum policy.
It is currently stalled by a High Court challenge over its legality.