I've been happy to find out recently by comparing tires, after MudB8 put me onto this idea (which he's been using for years)...
That there are some tall skinny tires available that are (IMO) aggressive hybrids that are good onroad and offroad.
Namely Trxus MT. They are really an aggressive hybrid IMO, and best of all, they run tall and skinny compared to their stated size, and especially compared to other brands.
For example, MudB8 owns both Cooper STT (which he's not fond of), and Trxus MT (which he loves).
His STT stated size is 35 X 12.5, but run shorter and wider than that. They're really more like a 34 X 13.
His Trxus stated size is 34 X 12.5, but run taller and narrower than that. They're really more like a 35 X 11.5. Hot dam! That's the stuff! I love tall narrow tires.
Now get this, in a side by side comparison, Dave's (Mud's) Trxus are an inch taller, and an inch narrower than this STT.
Eureka! I love that about the Trxus.
So for the OP, if you get some 34 X 12.5 Trxus, you'll really be getting a 35 X 11.5 tire (available in R15 and R16). That's pretty close to what you want, and in an excellent aggressive hybrid tread that is relatively good and quiet onroad and kicks butt offroad, and on winter roads too.
Now if you really must have a 35 X 10.5 wide, Interco's more aggressive tires like Super Swampers or others might well come in that size, but keep in mind, Interco typically runs tall and narrow compared to stated size (a good thing, IMO).
I also know that Simex makes Extreme Trekkers in 35 X 11 R15 and R16 if you really must have that exact size. However, Simex tires run taller that stated size (even more than Interco). So to get what most Americans consider a 35" tire, get their 34" size. Their 35" size is really a 36" tire. However, the Extreme Trekker will be poor on road (similar to a Super Swamper on road, but even better offroad).
If you want a tall skinny tire that will work onroad as well as offroad, then I think Trxus can't be beat. For honorable mention though, the MTR-K run about typical to size for stated height, but they do run 1/2 narrower than stated size. Narrow is a good thing, IMO. However, the Truxus are running more like 1" narrower than stated size, which is even better, IMO. One good thing about the Trxus, and even-more-so about MTR-K is that they last longer than hyper-aggressive MT (and work better onroad too).