I have a Rose DX Cross which is about 10 years old.
It has Ultegra 6800 2x11 gears.
I would like lower gearing for off road climbs.

The inner ring is 34t. The cassette is 11-32.

Can I make my life easier or do I need to be more Arnie?

You should be able to fit a sub-compact chainset, or even a MTB double chainset to get a lower range. You could also go for a bigger cassette (11-36, 11-40 or even 11-42) but might need a goat link or similar to clear it at the rear.

Mtb crankset
42.rear cassette ( I don't know what shimano can take)
I run a 50/34 with 42 cassette (.can just get away with a 46 but it's sub optimal)

I'd start with a different cassette; relatively cheap (even if you need a hanger extender), and doesn't mess up other components.
If going down the MTB chainset route, don't be surprised if your front mech doesn't play nicely. My XT double needed an offset shim for a road mech to work. It now has a GRX front mech which can cope with the extra reach due to its slightly more outboard chainline.

Nothing wrong with going smaller. Some people have mocked me for the Alpine gearset I run for hilly places. They might be able to spin faster at the top end, but you will be much more comfortable on a loaded bike on the hills or off road.

Sounds like a larger cassette and a goatlink will sort me out

May not need a goat link may as a longer b screw may be enough, depends how much bigger you go ( and what the max is for your mech)
For.sram you can use a mtb mech (.10?speed one.for 11 sped shifter).no idea with shimano

Update

In the end I got a 42t Microshift cassette and a Shimano GRX 2x111 (RX810) derailleur off of the CRC close down sale.
Fitted them today and shifting is nice and smooth. Although the maximum cassette for that mech is meant to be up to 40t, the 42t is no problem and didn't require a goatlink or longer b-screw

yourguitarhero wrote: ↑Sun Mar 24, 2024 10:25 am Update

In the end I got a 42t Microshift cassette and a Shimano GRX 2x111 (RX810) derailleur off of the CRC close down sale.
Fitted them today and shifting is nice and smooth. Although the maximum cassette for that mech is meant to be up to 40t, the 42t is no problem and didn't require a goatlink or longer b-screw

Shimano tend to be a bit conservative with their max sprocket size - it's probably so they get less consumer problems in pushing things to the limit. I've gone two larger than the recommended max tooth count with no problems (and not needing any shenanigans like reversing the B-screw or longer B-screw or goat link), some have gone four larger and been OK but it's not something I've done.