Is this heterocyclic boron molecule aromatic? What kind of aromaticity does the following molecule have?



I read somewhere that this is  an aromatic compound, but I believe that in order to be aromatic, it should have continuous resonance. I also think that there should be a break at B that causes no $\pi$ electrons to be shared among the B—B atoms...so I think this is non-aromatic. Is that correct?
That molecule is indeed aromatic.

It satisfies Huckel's rule ($4n+2$) with $n=0$. It's also planar.

Lastly, the boron atom has three electron domains, meaning it can exist with $sp^2$ hybridization. The left-over p-orbital, whilst not actively forming $\pi$  bonds, can still complete a stable $\pi$ molecular orbital.