I am referring to both the design, and the independent, and auditable manufacture of the CPU. It should be noted that such a CPU needn't fully compete with modern ARM, Intel, AMD, etc. CPUs, but it would be an incredible boon to have a fully trustworthy piece of hardware, even if it is considerably lower in it's strength. For specifics, let's say a CPU that could run a lightweight Linux distro at a "tolerable" speed.

Creating the designs for the CPU, of course while still difficult, is, most likely, the most feesbile aspect -- I presume it would "just" consist of writing the Verilog, or some other hardware description language to describe the CPU's function. The manufacture, however, is a substantial obstacle. Modern photolithography is, quite litterally, at the very forefront of human technological creation. I am just hoping that turning back the clock perhaps 20 years on the technological complexity might reduce the barrier to entry.