This is such a great question, in my opinion, because I think the concept of what's a "splurge that is independent of cost" is really relative and situational from person to person.
So, some folks don't think twice about dropping $500 on a pair of amazing and well made boots that they know they'll wear for years (I'm totally guilty of this. But if you consider that I purchased my oldest pair of Frye engineer boots over 25 years ago and I still wear them all the time, the actual cost over time was really low).
This is also true of the numerous other pairs of "high end" boots and leather jackets that are in my closet. I wear them all the time for years (because most are pretty classic in their style/cut or I just don't care if they're considered "fashionable" by society's standards).
So I didn't think twice about snagging a new pair of Frye Jenna Skull Leather boots when a brand new pair came up on ebay in my size for $300 (they're $600 at all the ecommerce retail sites that sell them). Some folks would have called that a splurge and I called it a bargain.
So, to me, if I were going to splurge on an item and cost was not at all a consideration I would want something that was unique, that not everyone else has. So, a designer bag would be out, for example, simply because it's not unique enough. I would also want it to be something I will wear very often, so versatility is a big factor in deciding whether to splurge (again, going back to the concept of cost per wear).
For me, this would be represented by either a very unique piece of antique/vintage jewelry that is well above the price point I normally spend at (I used to deal antique jewelry and vintage clothing when I lived back east and there were definitely a few pieces that I wish I'd had the luxury of keeping instead of reselling) or an incredibly unique piece of jewelry that is really representative of my rather quirky style and is made by an artisan jewelry designer. So it isn't mass produced.
Most of you may find this creepy but I have, for many years, loved skull and anatomy related stuff (long story as to why, mostly having to do with remembering that at some point we're all going to die so it's important to remember to live, and I find it interesting that these have now become trendy in recent years). So my splurge would likely be something by this jewelry designer: http://www.kimericlilot.com
In particular, I would really love to own this particular ring largely because it meets my criteria for "cost not a factor big-time splurge," (it costs just under $5k) I would wear it all the time, and the symbolism of it resonates with me (there's an element of memento mori jewelry and remembering to think about enjoying life while we're here: http://www.kimericlilot.com/ring16/
This was such a great question. I really enjoyed how much it made me think about what really is a "no cost consideration splurge" for me. And the replies really made me think a lot about how personal and subjective such a thing is! I'm new to the community and I really love how everyone's conversations seem so supportive and thoughtful!