First, none of the factory pickups have enough oomph to tow a 35k trailer. Even the class 5 trucks aren't enough.
For example, Ford F-550 chassis cab with the special order only high capacity trailer towing package and with aftermarket tow body has only a 26,000 pounds tow rating. So you're looking at a minimum of a class 6 chassis cab truck with aftermarket tow body (or flatbed with a 5er hitch).
So as a minimum look at Class 6 chassis cab trucks from Freightliner, Peterbilt, Kenworth, Mack. Study the specs and order one with enough oomph to not only pull 40k but to also haul up to 10k hitch weight at the same time.
Mountain Master is a custom truck builder that will build you a tow vehicle that can tow your trailer without being overloaded. Not cheap, but safe and reliable. Here is link to their Freightliner custom trucks: (They also can build a Ford F-650 to your specs.)
Mountain Master Exterior
Sport Chassis converts FreightLiner medium-duty trucks by adding a pickup bed, tow body or flatbed with 5er hitch to a chassis cab truck.
Here is a link to SportChassis RHA 350 on a Freightliner M2-106 chassis:
I don't see the towing specs on that website, so go to the Freightliner website and get the towing specs for the M2-106 chassis.
Here is a link to SportChassis RHA 450 on a Freightliner M2-112 chassis. Plenty of tow vehicle for your needs, but note you will need a CDL with air brakes endorsement to drive this tow vehicle:
And finally there are lots of folks that insist on a retired OTR class 8 truck (HDT or heavy duty truck/tractor) to economically tow that much trailer. That retired but overhauled HDT with less than a million miles on the clock will cost a lot less than a new Mountain Master or Sport Chassis medium-duty truck (MDT). And with a proper overhaul/rebuild, it should last you another half-million miles towing only 40k, which is only half it's designed towing capacity..