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Never had brown pudding, but got curious what it was and see it's essentially brown sugar and flour - with some butter and milk.
There are online suggestions for brown sugar substitutes (methinks Shanny has one), and for the flour you could use almond meal with some flax meal, but it does look like a challenge.
For some things there just is no substitute, like my risotto. A month or so ago I talked a friend into ordering something with risotto so I could have a bite
He did, and once I was nice and satiated I took a couple of bites and stole a strategy from someone here who said they then pretend their satiety is because of that last bite. It works in an odd way - maybe tricking yourself is easier after a glass of wine 
Good luck!
There are online suggestions for brown sugar substitutes (methinks Shanny has one), and for the flour you could use almond meal with some flax meal, but it does look like a challenge.
For some things there just is no substitute, like my risotto. A month or so ago I talked a friend into ordering something with risotto so I could have a bite
Good luck!