The concept of Brut IPA is not even two years old, yet. So, it's still evolving as a style. To me, it's more of a technique than a style, but that's how I view Cal Common, too.
What sets it apart is the use of adjuncts plus enzymes in the mash and fermentation to increase the fermentability, decrease proteins and generally vanish the malt character. What's left is hop character carried by alcohol. The hop character is supposed to show the effects of bittering, late WP, then early and late dry hop, while being bone dry, effervescent and brilliantly clear.
This article discusses how Kim Sturdavant started the technique. https://beerandbrewing.com/the-birth-of-the-brut-ipa/
The irony is, that to be made well, the brewer must embrace the same technology and wort manipulation long practiced by the mass lager companies, that most vow to hate. Adjunct grain and enzymes are the keys to this emerging style. Another irony is that some assume champagne yeast is required when it is not. In fact, the esters and fusel alcohol of champagne yeast can get in the way.
Long ago, I accepted the fact that brewers are early adopters of technology and push the boundries of malt's willingness and flexibility for making beer. After all, by 1855, lager breweries had mostly accepted that pure yeast strains were making better beer (sort of an early germ theory) and that microbes could ruin it. However, in 1865, surgeons were still wiping knives on their shirt sleeves in open sided tents during the US civil war.
I make a Brut with corn (instant grits) and three types of enzymes. I get pungent hop aroma and complex hop flavor, along with just about double the shelf life of my primary DIPA. There's also Munich malt which is transformed into wonderful crusty bread flavor without the usual sweetness. A benefit of amylase enzyme is you can use crystal malt because it'll break down dextrine and leave the flavor.
Attached is my first recipe for Brut.