bread and butter

  1. We had bread and butter with our breakfast.
  2. We had bread and butter in our breakfast.
    Are both sentences OK?
    What is the meaning of ‘Fine words butter no parsnips.’?
    Thanks.

The second is incorrect and the first indicates that the bread and butter wasn’t actually part of the breakfast, so no to both.

We had bread and butter for breakfast.
We had bread and butter as (a) part of our breakfast.
Our breakfast included bread and butter.

Have you tried using a search engine to find the meaning of “fine words butter no parsnips”?
There should be no need to ask, you could be independent in finding the answer. To be certain that you’d be able to find the answer easily I tried it myself. I used Google and the key phrase
define fine words butter no parsnips
but I think
meaning fine words butter no parsnips
would work just as well.
You will find the meaning for yourself quite easily if you do that,

Why did you drop the ‘our’ here? Any grammatical reason?

No. It’s unnecessary and less natural so I omitted it as I would in standard conversation.

Then why here?

Different preposition.

Not digesting. A proposition, perhaps!

Perhaps you should change your diet.
‘For’, ‘of’ and ‘as’ are prepositions.