I do this exact cook very often to create roast beef sandwiches.
I start with smoking at 225 -275 on the BGE. until 105deg internal. Then I sear over direct heat on all sides around 700 degrees until it reaches 115. I let it rest for 30 - 40 minutes at room temp so it cooks itself to about 120-125 internal. Then it goes into the fridge until the next day or the evening. After it rests and is completely cool, I slice it paper thin on the slicer.
Top it off with sauteed onions & peppers w/sharp provolone. I usually put a small dish of au jus on the side for dipping. Makes killer sandwiches.
2013 Stumps Classic - Delivered 4/15/13
Large BGE - Rescued 2012
2010 WSM 22.5"
2010 Weber genesis gas grill
Rescued 22.5 Weber One-touch gold
BBQ Guru CyberQ
2011 Built UDS - Retired