Every day I do the cooking
The verb do is used in the present tense. The present simple is normally used to express daily routines, actions and habits which are repeatable in the present and in the future. The simple present is often accompanied with frequency adverbs such as: usually, often, sometimes, hardly ever and never. For example,
I never do the cooking, my partner does.
The present participle i.e., doing, with the time expression every day is possible in the following scenario:
I'm doing the cooking every day
Every day I'm doing the cooking
The time expression every day has the same meaning as the frequency adverb always. It matters little where every day is positioned in the phrase, it can either begin or end the clause. Instead of always, other words with similar meanings (e.g., forever, constantly, and continually) can be used.
always doing the cooking
continually doing the cooking
In all four examples the speaker can be expressing their irritation at having to perform a daily or oft repeated duty/chore. This type of construction expresses annoyance in the present. If you are simply stating a fact then use the simple present instead.
always do the cooking
I do the cooking
If you want to express future intent, use a different time expression such as:
Tomorrow/this week/on Saturday I'm doing the cooking.