Use a CPU that does constant-time everything (e.g. has no caches). Most of the super-simple in-order RISC-V cores that are available on github will do. Just put one of them in an FPGA, and you are set up.

Most of those CPUs are designed by CS or EE students taking a computer architecture class, so... in a sense... one can argue that defending against Spectre-like attacks is actually super simple: just use a simple CPU design.

To actually become vulnerable to Spectre, you need a very complex CPU design, so in the same way, it can be argue, that making a CPU vulnerable to Spectre is actually hard, since it takes a lot of work to create such a CPU design.

Now, if what you want is a CPU that's both fast and secure, then I'm sorry to tell you that such thing cannot exist. Those two goals are at tension. You can either get a F1 or a tank, but no vehicle that offers the same amount of protection as a tank is going to be able to compete against a F1 car, and vice-versa.