Is there a way to set a global DNS server that will be used for all connections (both Wi-Fi + cellular data)? If there isn't a uniform manner to specify DNS, can I just change the DNS used by the cellular connection?
Ideally, I am looking for an answer for vanilla iOS; however, I'd welcome any solution, including one that requires a jailbreak.
Yes, there is way. And since you're already jailbroken, it'll be so much easier. Just open up Cydia and search for GuizmoDNS. It's from the ModMyi repository, which comes preconfigured with Cydia. It allows you to select the DNS server to go through when using a cellular data network, and it does it right from the Settings app.
I'll cover the no-jailbreak scenario and leave editing or another answer for someone that knows how to change this by modifying iOS.
Without a jailbreak, no. The cellular data is governed by APN settings. You can change these with the iPhone configuration utility and some learning.
The Wi-Fi settings are easy to override using the device itself, but it's not global but instead an override on a per-network name basis. Go to the network settings for a specific Wi-Fi. Under the detailed screen (tap the blue > sign once you are connected) and swipe up to expose the DHCP / BootP / Static IP address part of the screen. You can tap to edit DNS and append, delete or substitute your choice of DNS settings from that screen.
When I need to run a custom DNS, I often use VPN to get to a router with known settings and this works over Wi-Fi and cellular data since all traffic goes to the VPN where I can control the DNS. This requires time and a server (Amazon web service free tier is ideal for low cost hosting).
You can use this app: https://www.dnsoverride.com/ It can override DNS settings for any Wi-Fi and cellular connection. One scenario in which it's not going to work is if your ISP intercepts DNS traffic. Some mobile operators do.
