No experience, but I think this is more reachable than it was years ago (at least in prototype form). I haven't done a recent survey and there might be better

No experience, but I think this is more reachable than it was years ago (at least in prototype form). I haven't done a recent survey and there might be better options now, but... I'd start with basic FPGA development with a hobbyist board (an Alchitry or Arduino Vidor or somesuch), learn a hardware description language, play a bit and then look as some open source CPU designs. There are a few open source designs with very low LUT (lookup table) counts, I'd probably start looking at those. What I have in mind is something super-simple, just enough to be able to implement a single object or function. I'm aiming at mapping a high-level language almost directly to gates. I don't have much of a plan for the interconnects yet, but I'm sure there should be some simple scheme I could start with. I'm not sure about actually getting to an ASIC chip, I'd probably just end up going for the biggest FPGAs I could afford or finding ways to interconnect a few smaller ones.