It took some time searching around but I finally managed to find an answer by myself, I'm posting the solution here in case anyone has a similar issue:
Open Sound panel
Select Speakers as the default playback device
Go to the "Recording" tab
Right click and enable "Show Disabled Devices"
A recording device called "Wave Out Mix", "Mono Mix" or "Stereo Mix" (this was my case) should appear
Right click on the new device and click "Enable"
Right click on the new device and click "Set as Default Device"
Double click on the new device to open the Properties window
Go to the "Listen" tab
Click on the "Listen to this device" checkbox
Select your HDMI device from the "Playback through this device" list
And you're done, the drawback is that you won't have a microphone selected as default recording device, but for what concerns me I couldn't care less.