Putting aside why you'd want to do this, it'd be pretty easy, actually. You'd still use a big model like GPT4 or Claude as your "base" but you would do two things:

• Give it a knowledge base using your conversatons. You can manually vectorize them into a key-value database like Pinecone and build yourself an agent using a toolchain like Langchain, or just use a service (OpenAI Agents lets you upload data from your browser)
• Have one of the big LLMs (with a large context size) ingest all of those conversations and build out a prompt that describes "you"

you would then

• Feed that generated prompt (with your own edits, of course) back into either your custom Langchain agent or OpenAI Agent