Which version of openssl gets installed if you don't specify the version number?
The error you mentioned in the issue says Python requires a OpenSSL 1.1.1 or newer and it seems odd to me that it would install an older version by default and require a pinned version to get a newer release. I wonder if that error is wrong 🤔

@ezio-melotti that is a very good point. I uninstalled openssl brew uninstall openssl, and verified that I would get the same message when compiling:

The necessary bits to build these optional modules were not found:
_hashlib _ssl

as well as

Python requires a OpenSSL 1.1.1 or newer

I then ran brew install openssl. This time it worked, it installs openSSL@3 the latest version. The message above didn’t show. I am sure though (I can still see it on the terminal), that installing openssl the first time, and following the instructions, lead to the message above. I believe that even though I uninstalled openssl, the uninstallation didn't remove all the files that were created when installing openssl1.1. I am therefore making this pull request purely about the warning issue and not the ssl module. I updated the related issue accordingly. If you think it is not out of the scope of the documentation, I will create a new issue and pull request, updating the documentation by adding a note saying that user might need to specify the latest version of openssl to be able to build the ssl module successfully. Let me know what you think.

Did you check which version of openssl gets installed by default (you can use openssl version to check)? FWIW on Linux I have OpenSSL 3.0.2 15 Mar 2022 (1.1.1 is from 2018-09-11 and 3.0.0 from 2021-09-07).
You could also try to run make clean or make distclean and then run ./configure and make again to start fresh and see if anything changes.

python/cpython#91357 (comment) might also be relevant -- maybe you were missing the libssl-dev package before? (cc @tiran)

@ezio-melotti It might be related but I have no quick way to check for sure now that I can't reproduce my issue in the first place! libssl-dev appears nowhere in my terminal. If I do a search on my laptop, I can find libssl.1.1.dylib and libssl.3.dylib but they were created a month ago, so not related. I am using brew and not pip so the part of the documentation that needs updating would be different in any case.

Once this PR is committed I will create a new issue and PR as I suggested. And yes, I did run make clean and ./configure before make for each of my attempts. Thanks for suggesting it.

@ezio-melotti regarding the openssl version, it returns LibreSSL 2.8.3. This is why I believe the documentation says to run ./configure --with-pydebug --with-openssl=$(brew --prefix openssl).
If I run brew info openssl , I get:

openssl@3: stable 3.0.3 (bottled) [keg-only]
Cryptography and SSL/TLS Toolkit
https://openssl.org/
/usr/local/Cellar/openssl@3/3.0.3 (6,441 files, 28.3MB)
Poured from bottle on 2022-06-10 at 10:37:27
From: https://github.com/Homebrew/homebrew-core/blob/HEAD/Formula/openssl@3.rb
License: Apache-2.0
==> Dependencies
Required: ca-certificates ✔
==> Caveats
A CA file has been bootstrapped using certificates from the system
keychain. To add additional certificates, place .pem files in
/usr/local/etc/openssl@3/certs

and run
/usr/local/opt/openssl@3/bin/c_rehash

openssl@3 is keg-only, which means it was not symlinked into /usr/local,
because macOS provides LibreSSL.

If you need to have openssl@3 first in your PATH, run:
echo 'export PATH="/usr/local/opt/openssl@3/bin:$PATH"' >> ~/.zshrc

For compilers to find openssl@3 you may need to set:
export LDFLAGS="-L/usr/local/opt/openssl@3/lib"
export CPPFLAGS="-I/usr/local/opt/openssl@3/include"

For pkg-config to find openssl@3 you may need to set:
export PKG_CONFIG_PATH="/usr/local/opt/openssl@3/lib/pkgconfig"

==> Analytics
install: 137,635 (30 days), 449,281 (90 days), 995,856 (365 days)
install-on-request: 113,094 (30 days), 363,685 (90 days), 791,601 (365 days)
build-error: 4,447 (30 days)