So this is typically what BGP is for, but this is definitely not something that is typically offered to residential customers, nor even most business AFAIK. This is what you would typically get with a Direct Internet Access (DIA) connection. This is an uncontended connection where to setup a BGP peering with your provider. You then give the provider some documentation proving you own a range of addresses, and they agree to accept those routes from you via the BGP connection. They then advertise that to their upstream providers, and thus the routes propagate to the entire internet.

There are a couple of gotchas though. Firstly, there is generally a minimum prefix size of routes that will be accepted into the global routing table. For IPv4 I think it is a /24, and for IPv6 I think it is a /32. You can get a /32 from regional IP registry (for free?) but you will probably need to become a member which – last time I checked - costs 3-4 figures a year. You can use a private-AS number though, as you'll only have one upstream provider.

The other gotcha is cost. Depending where you are in the world, a DIA connection will cost in the very rough region of (EUR/USD/GBP) 1/megabit/month, although it becomes much cheaper when going from 1gb to 10gb.

Now maybe there is some cool facility that some nice ISPs offer to bypass all this, if so then please let me know. I'm personally skeptical it would be worth their while for the 0.001% of residential customers that would want this service though.

Source: I run a small ISP. I have some industry knowledge, but not loads.