How to handle time consuming search requests

We're developing a search functionality for our product (web). We are having some controversies how to handle search requests that can take up to one minute.

Current version: After clicking enter or after hitting the search button, a loading animation starts and the whole screen gets blocked. You're not able to click back again in the input field or anywhere else on the application except the user settings and the logout button until the request is handled.

That's how we used to do it with all filter/search functions, but they weren't as time consuming, so it never really bothered us.

I really don't like the blocking mechanism and that you can't send another search request in case you want to correct a typo or such.

What can we do to avoid making the user wait until the request is finished in case the search entry was wrong and needs to be changed?

Thanks for your help.

For visualization: