Learn Finnish: Minulla on tapana mutista, kun teen töitä. - I have a habit of muttering when I work.

It is a fixed construction expressing a habit. It requires the person who has the habit to be in the adessive case (minulla), followed by on tapana (literally 'is as a habit'), and then the main action verb in its basic dictionary form, the first infinitive (mutista).

Why is the word 'tapa' (habit/custom) in the essive case (tapana) instead of the nominative?

The essive case ending -na typically translates to 'as a'. While minulla on tapa just means 'I have a habit', using the essive turns it into the descriptive state 'as a habit'. This makes minulla on tapana the natural, idiomatic way to say 'I am in the habit of' doing something.

Why is the word for work (töitä) in the partitive plural?

The phrase teen töitä (literally 'I do works') is the standard way to express the ongoing action of working. Using the partitive plural (töitä) shows that the action is continuous and doesn't have a clear endpoint. If you used the accusative singular (teen työn), it would mean you are completing one specific, defined job.

Could I use the verb 'tavata' to express this same habit?

Yes, you could! At B2 level, you might already know that the verb tavata means 'to meet', but it also means 'to have a habit of'. You could say minä tapaan mutista, which means the exact same thing as minulla on tapana mutista.