I make this at the bar I work at and it is truly a big hit.
Adding cold cheese directly to boiling liquid causes proteins to seize and fats to separate into an oily slick. Achieving a smooth emulsion requires managing dairy proteins and starch ratios carefully. When building the base, cook the flour and oil mixture for a full minute to eliminate the raw taste of the grain before introducing the half-and-half.
Shredding blocks of sharp cheddar, pepper jack, and blue cheese by hand prevents the anti-caking agents found in pre-bagged varieties from interfering with the sauce. Whisk the cream steadily into the roux while simmering over medium-low heat until the liquid reduces by one-third. Remove the pan entirely from the heat source before stirring in the cheeses to ensure the residual warmth melts them smoothly without breaking the emulsion. Adjust portions proportionally when scaling quantities up or down, keeping the ratio of flour to dairy consistent to maintain proper thickening power.