> My question is with regard to taxes, if I am selling upon vest every other vest period does the brokerage determine which shares I am selling?

Default cost basis accounting is First In First Out (FIFO). You can change it to specify which shares to sell.

> Is it possible to sell the newly vested shares only so I am not paying cap gains on the shares I am holding?

Yes. Switch to Specific Identification (Spec ID) or Last In First Out (LIFO) or Highest Cost First Out (HIFO) or Tax Optimized or whatever else the brokerage offers that makes sense.