Appraiser
Appraisers hold a state license or certification and write the value opinion a lender relies on before it funds a loan. In BRRRR the appraiser sets the after-repair value that sizes the cash-out refinance, so one person's opinion decides how much of the investor's cash comes back.
Lenders order the appraisal through a management company, so the investor does not choose the appraiser. What the investor can do is make the case easy to see: a list of completed work with costs, permits, and recent sales of similarly renovated homes nearby.
On the default deal, each $10,000 of appraised value is worth $7,500 of loan at 75% loan-to-value. A value $30,000 short of plan cuts the cash out by about $21,800 after costs. Most lenders allow a reconsideration of value with better comparable sales, but it rarely changes the number by much.
Further reading: Appraiser on Wikipedia.