You'll need some way to end the game, as swinging for 1 with him over and over seems not ideal. In mono blue your options are basically some kind of big storm payoff (very hard to do with brain freeze given deck sizes), or setting up some sort of infinite combo, mana, extra turns, whatever. Creature based plans seem not great in mono blue aside from just ramping up to like a blightsteel or something, but that feels pretty flimsy for EDH.
Planar portal + beacon of tomorrows is the age old blue combo standby if you want to go that route. Otherwise there's plenty of options to make infinite (or near enough) mana with various urza free spells/high tide/isochron scepter etc.