Shalom and thank you for your interesting question! There is no problem with learning Torah while you cook. In fact, by doing so, you are elevating the mundane act of cooking to an  even higher level. Cooking in itself can be a mitzvah if done to maintain the health and wellbeing of yourself and your family, or as a source of  honest income. When you are exposing yourself to a holy influence such as a Torah class, you are elevating the experience and even the physical objects you are dealing with to an even higher level.

The Talmud tells of a woman who would bring her baby to hear the study of the sages. She merited that he became a well-known sage, Rabbi Yehoshua ben Chananiah. His teacher Rabbi Yochanan ben Zakkai attributed the greatness of Rabbi Yehoshuah to the influence he received as a baby by being exposed to Torah learning from such a young age, and he praised the mother for this. The point here is that at any age or stage it is a very good thing to be surrounded by Torah learning. It is a positive influence for body and soul.

There is an additional point to be taken into consideration. Every Jew has a duty to learn Torah. The duty for men is constant. “And you shall speak them (words of Torah) day and night”. (Book of Joshuah 1:8) This means that Jewish men are obligated to spend as much time as possible in the  twenty-four hours actively learning Torah. The Torah recognizes that not everyone has the possibility to spend all their time learning, whether due to their intellectual make-up, their character, the need to earn a living, or a combination of the above. Thus there is a minimum. In the order of the morning blessings there is a passage from the Mishnah, and this together with learning another passage in the evening, constitutes the basic minimum so that a man can easily fulfill his obligation to learn Torah day and night. The Tanya, a basic text of Chassidic teaching, teaches that we must take into consideration the nature and circumstances of each person. Nevertheless a person must always strive to improve his or her spiritual standing and try to gradually increase the amount of Torah that is learned, for the Torah is the Divine will and wisdom, and by learning it we connect with G-d. A Jewish woman is obligated to learn all the subjects which relate to the mitzvot which she is obligated to do. These include laws relating to Sabbath and festivals, the observance of kashrut, family purity, tzedaka, and mitzvot that are called ‘constant mitzvot’ such as working on love and awe of G-d, among others. Learning Tanach and Chassidic philosophy and the various broad Torah literature that brings one to love and awe of G-d are all conducive to this.

Thus, if there is time to attend a Torah class or learn from a book by yourself or with a friend even when you are not necessarily occupied with some other task, this can only be a positive thing. Perhaps you are familiar with the practice of learning Chitas, which stands for Chumash, Tehillim and Tanya. This consists of learning the daily portion from the current weekly Torah portion, saying the daily portion of Tehillim as they are sectioned off for the days of the month, (the book of Tehillim or psalms is divided into sections for the days of the week, or sections for the days of the month,) and learning the daily portion of the book of Tanya which is mentioned above. You can look this up on Chabad.org. or consult your nearest Chabad emissary. In any case, any topic in Torah which interests you is a good thing to learn, and it is very good to make a practical commitment such as deciding to learn one Halacha a day from a section of  Halacha dealing with a topic you want to know more about or you feel you should brush up on. In the same way you could try to learn a paragraph a day from a book of Chassidic teaching or read a story about a righteous person. There are endless possibilities because the Torah is endless, and when you learn Torah you are drawing down Divine light into this world.

Torah is also something which should be shared, and since your question indicates that you are already involved in Torah learning, you can share that with others. Even if you don’t think you know that much, you can still share what you do know and inspire another Jew to connect with G-d.

Wishing you much success in all your endeavors!