"most recently that" is correct and can be used in written English.
It is used to indicate that something happened recent in comparison with something else. For example: "I have seen him three times this year, most recently that was last week."
Most recently, that statement referred to her position on last September's Scottish independence referendum.
Most recently, that has been especially true with the weak housing data.
But it's the companies that are associated with them — like Chipotle, most recently — that suffer the PR blow.
Most recently that has led to Pat Fili-Krushel gaining command of all of NBC's operations in news.
Most recently that has been represented by proposals for a Jewish nation state law and by Lieberman's plan to transfer Israeli-Arab citizens en masse out of Israel into a new Palestinian state.
Most recently, that crop has included raspberries and loganberries from Scotland, which produces some of the best in the world: they're a great addition to pillows of sweetened, whipped ricotta in my easy version of peach melba.
"People will start picking things that have gone up the most recently, and that is a terrible choice.
But he added that he had participated in seven Congressional hearings, most recently last week, that focused on problems with how the defense and veterans departments track medical information.
Agarwal has started up a lot of start-ups, most recently one that made multicore processors.
It is very likely Groh will want to talk to Ray Hamilton, a former Jets' defensive line coach, who most recently had that role on the Patriots.
Most recently, plants that produce parts for the Japanese automakers Honda and Toyota have been hit by labor shutdowns.
