The plans, which have been submitted by Brad Hanson and Sam Hughes, known as the Bald Builders, are due to be considered by Arun District Council on June 23.
If they are granted, the café, which will also have a coffee drive-thru round the back, will be built at the former Bairds Farm Shop.
Brad, 37, who lives in Littlehampton, said: “We are very excited for this new journey. We have taken a gamble on it, having sold our usual The Bald Kitchen on wheels.
“We outgrew this wagon due to demand.
“We can’t wait to get started and to be serving customers again.”
Brad said he and Sam, his brother-in-law who lives in Felpham, have been going on coffee courses to learn how to make a ‘proper cup of coffee’.
They plan to serve their own Bald Blend, using local barista Edgcumbes in Ford Lane, Arundel.
And they will support local businesses to supply ingredients for the garden centre-style café, Brad said, such as meat from John Wildman & Sons Butchers in Rustington for their famous 60z burgers and eggs from Rookery Farm in Felpham.
Brad added: “It is not going to be fast food, but more about afternoon teas and scones and of course, coffee.”
Brad and Sam have a 40ft shipping container which they will convert into The Bald Kitchen if planning permission is granted.
They sold their previous wagon to Chesterfield Royal Hospital which is now being used in the hospital’s car park to serve staff and patients.
The comedy duo, who have racked up millions of online views of their videos, started The Bald Kitchen to put Littlehampton’s food scene on the map. The location changed each day between Bognor and Littlehampton.
The pair also try and give back when they can. They recently raised £2,500 for mental health charity, Mind.
But despite their enthusiasm for this new project, not everyone is as happy about the plans.
Karen and Keith Halsey said: “We believe it is out of character with the local area of Climping. Also it is likely to cause an increase in traffic.”
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