It depends whether your hypothyroidism condition is due to a natural progression of your thyroid failing, or whether your hypothyroidism is caused by exogenous factors e.g drugs, or certain foods. If it is the latter case, then avoiding certain drugs, or certain foods may restore thyroid function. Yet in some cases, e.g exposure of to radiation, can cause thyroid failure as well. So in general, the "cure" would depend on what kind of hypothyroidism that you have.

Hashimotos

I am sorry to hear that you have Hashimotos. Do you have primary or secondary Hashi? It is an autoimmune condition, so you probably have thyroid antibodies, as your immune system is attacking your thyroid gland. I am supposed to have Hashi, but 8 years have passed and my thyroid is functioning well.

You can improve your thyroid health by avoiding food that trigger a flare. Look at the Hashimoto diet, eat plenty of fruits and veggies because these are rich in antioxidants so they will reduce inflammation of your thyroid. My thyroid function is quite good despite the pending Hashi diagnosis. By looking after yourself and your diet, you may improve your thyroid function. Best wishes, and good luck!