I recently built a new machine with the i7-5820K Haswell-E 6-Core CPU which sells for $350. It requires an LGA2011 socket motherboard which costs a little more than an LGA1151, but it can easily be overclocked to ~4 GHz and compares well against the i7-6700K Skylake 4-Core CPU in benchmarks.

https://www.cpubenchmark.net/common_cpus.html